TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems

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DOI10.1016/0021-9991(89)90183-6zbMath0677.65093OpenAlexW1982465309MaRDI QIDQ1123565

San-Yih Lin, Chi-Wang Shu, Bernardo Cockburn

Publication date: 1989

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://purl.umn.edu/4838

zbMATH Keywords

numerical results conservation laws nonlinear systems Galerkin finite element methods total variation bounded Runge-Kutta local projection

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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II: Two dimensional case, Discontinuous Galerkin method based on non-polynomial approximation spaces, Runge-Kutta discontinuous Galerkin methods for compressible two-medium flow simulations: one-dimensional case, CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation, Parallel structures and dynamic load balancing for adaptive finite element computation, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, A numerical comparison of the Lax-Wendroff discontinuous Galerkin method based on different numerical fluxes, High-order accurate discontinuous finite element solution of the 2D Euler equations, Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results, A Runge-Kutta discontinuous Galerkin method for viscous flow equations, One-sided position-dependent smoothness-increasing accuracy-conserving (SIAC) filtering over uniform and non-uniform meshes, Energy conserving local discontinuous Galerkin methods for the nonlinear Schrödinger equation with wave operator, Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case., Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws., Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes, Spectral (finite) volume method for conservation laws on unstructured grids. IV: Extension to two-dimensional systems., Discontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water., Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations., A discontinuous Galerkin solver for Boltzmann-Poisson systems in nano-devices, The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations, A DGBGK scheme based on WENO limiters for viscous and inviscid flows, A space-time discontinuous Galerkin method for Boussinesq-type equations, Discontinuous element pressure gradient stabilizations for compressible Navier-Stokes equations based on local projections, Computation of compressible flows with high density ratio and pressure ratio, An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and \(L_2\) stability, A second order discontinuous Galerkin fast sweeping method for eikonal equations, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes, High-order finite volume methods and multiresolution reproducing kernels, A robust discontinuous Galerkin method for solving convection-diffusion problems, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, Fourier analysis for discontinuous Galerkin and related methods, An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws, Spectral (finite) volume method for conservation laws on unstructured grids. II: Extension to two-dimensional scalar equation, A discontinuous Galerkin method for the full two-fluid plasma model, An implicit high-order spectral difference approach for large eddy simulation, Multilevel and local time-stepping discontinuous Galerkin methods for magma dynamics, A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes, A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes, A short note on the error estimates of Yuan-Shu discontinuous Galerkin method based on non-polynomial approximation spaces, A spectral-element dynamic model for the large-eddy simulation of turbulent flows, A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation, Kershaw closures for linear transport equations in slab geometry. II: High-order realizability-preserving discontinuous-Galerkin schemes, Runge-Kutta central discontinuous Galerkin BGK method for the Navier-Stokes equations, Discontinuous Galerkin methods for plasma physics in the scrape-off layer of tokamaks, Energy conserving discontinuous Galerkin spectral element method for the Vlasov-Poisson system, Mass preserving discontinuous Galerkin methods for Schrödinger equations, High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation, A new spectral difference method using hierarchical polynomial bases for hyperbolic conservation laws, Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions, Hybridizable discontinuous Galerkin projection methods for Navier-Stokes and Boussinesq equations, Towards positivity preservation for monolithic two-way solid-fluid coupling, An adaptive finite volume solver for steady Euler equations with non-oscillatory \(k\)-exact reconstruction, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. I: The one-dimensional case, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. II: The two-dimensional case, An overset mesh approach for 3D mixed element high-order discretizations, An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods, A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids, Polymorphic nodal elements and their application in discontinuous Galerkin methods, High order multi-moment constrained finite volume method. I: Basic formulation, Mixed time discontinuous space-time finite element method for convection diffusion equations, A high-order discontinuous Galerkin method for 2D incompressible flows, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations, Local derivative post-processing for the discontinuous Galerkin method, Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows, The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems, Spectral/hp methods for viscous compressible flows on unstructured 2D meshes, Discontinuous Galerkin solver for the shallow-water equations in covariant form on the sphere and the ellipsoid, Controlling oscillations in high-order discontinuous Galerkin schemes using artificial viscosity tuned by neural networks, Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation, A discontinuous \(hp\) finite element method for convection-diffusion problems, An analysis of the discontinuous Galerkin method for wave propagation problems, Spectral (finite) volume method for conservation laws on unstructured grids. Basic formulation, RKDG methods with WENO limiters for unsteady cavitating flow, Explicit discontinuous Galerkin methods for unsteady problems, Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials, Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics, High order discontinuous Galerkin discretizations with a new limiting approach and positivity preservation for strong moving shocks, A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids, Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices, Arbitrary high order discontinuous Galerkin schemes based on the GRP method for compressible Euler equations, An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system, Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations, A hybrid LDG-HWENO scheme for KdV-type equations, Compact high order finite volume method on unstructured grids I: Basic formulations and one-dimensional schemes, Compact high order finite volume method on unstructured grids II: extension to two-dimensional Euler equations, Bound-preserving discontinuous Galerkin methods for relativistic hydrodynamics, High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments, An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations, Superconvergence of discontinuous Galerkin methods for hyperbolic systems, A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations, On discontinuous Galerkin approximations of Boltzmann moment systems with Levermore closure, Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations, The local discontinuous Galerkin method for linearized incompressible fluid flow: a review, An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods, Solutions of multi-dimensional hyperbolic systems of conservation laws by square entropy condition satisfying discontinuous Galerkin method, Discontinuous Galerkin method for hyperbolic equations involving \(\delta \)-singularities: negative-order norm error estimates and applications, Optimal convergence of discontinuous Galerkin methods for continuum modeling of supply chain networks, On the role of Riemann solvers in discontinuous Galerkin methods for magnetohydrodynamics, Implicit LU-SGS algorithm for high-order methods on unstructured grid with \(p\)-multigrid strategy for solving the steady Navier-Stokes equations, Strongly out-of-equilibrium simulations for electron Boltzmann transport equation using modal discontinuous Galerkin approach, A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems, High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws, A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations, A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies, Single-step arbitrary Lagrangian-Eulerian discontinuous Galerkin method for 1-D Euler equations, High-order discontinuous Galerkin method for applications to multicomponent and chemically reacting flows, Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations, A non-oscillatory multi-moment finite volume scheme with boundary gradient switching, Conservative DG method for the micro-macro decomposition of the Vlasov-Poisson-Lenard-Bernstein model, Energy conserving discontinuous Galerkin method with scalar auxiliary variable technique for the nonlinear Dirac equation, A discontinuous Galerkin approach for high-resolution simulations of three-dimensional flows, A second-order modified ghost fluid method (2nd-MGFM) with discontinuous Galerkin method for 1-D compressible multi-medium problem with cylindrical and spherical symmetry, An ultra-weak discontinuous Galerkin method for Schrödinger equation in one dimension, Discontinuous Galerkin methods with optimal \(L^2\) accuracy for one dimensional linear PDEs with high order spatial derivatives, A filtering monotonization approach for DG discretizations of hyperbolic problems, Compact high order finite volume method on unstructured grids. III: Variational reconstruction, Revisiting the spectral analysis for high-order spectral discontinuous methods, High order sub-cell finite volume schemes for solving hyperbolic conservation laws. II: Extension to two-dimensional systems on unstructured grids, Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations, An artificial neural network as a troubled-cell indicator, A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems, A fourth-order unstructured NURBS-enhanced finite volume WENO scheme for steady Euler equations in curved geometries, HODG: high-order discontinuous Galerkin methods for solving compressible Euler and Navier-Stokes equations -- an open-source component-based development framework, One-sided post-processing for the discontinuous Galerkin method using ENO type stencil choosing and the local edge detection method, A very-high-order TENO scheme for all-speed gas dynamics and turbulence, Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws, A hybrid finite element-finite volume method for conservation laws, High-resolution finite volume methods on unstructured grids for turbulence and aeroacoustics, A superconvergent discontinuous Galerkin method for hyperbolic problems on tetrahedral meshes, Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws, A hybrid mixed method for the compressible Navier-Stokes equations, Asymptotically exact discontinuous Galerkin error estimates for linear symmetric hyperbolic systems, A staggered semi-implicit spectral discontinuous Galerkin scheme for the shallow water equations, Analysis of a discontinuous Galerkin method for the Biot's consolidation problem, Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data, Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems, A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes, Limiters for high-order discontinuous Galerkin methods, An accuracy and stability study of the 2D spectral volume method, Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow, Local discontinuous Galerkin methods for the Cahn-Hilliard type equations, Efficient quadrature-free high-order spectral volume method on unstructured grids: theory and 2D implementation, A priori error estimates for interior penalty versions of the local discontinuous Galerkin method applied to transport equations, A spacetime discontinuous Galerkin method for scalar conservation laws, Spectral (finite) volume method for conservation laws on unstructured grids. VI: Extension to viscous flow, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws, The discontinuous Galerkin method with Lax--Wendroff type time discretizations, Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems, Spectral difference method for unstructured grids. I. Basic formulation, Building blocks for arbitrary high order discontinuous Galerkin schemes, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations, A Runge-Kutta discontinuous Galerkin method for the Euler equations, A local discontinuous Galerkin method for the Burgers-Poisson equation, A new approach for admissibility analysis of the direct discontinuous Galerkin method through Hilbert matrices, Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs, $L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations, High Order Positivity-Preserving Discontinuous Galerkin Methods for Radiative Transfer Equations, Maximum-principle-satisfying and positivity-preserving high order central DG methods on unstructured overlapping meshes for two-dimensional hyperbolic conservation laws, Superconvergence analysis of local discontinuous Galerkin methods for linear convection-diffusion equations in one space dimension, Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equa\-tions, Fourier analysis of local discontinuous Galerkin methods for linear parabolic equations on overlapping meshes, Discontinuous Galerkin methods for isogeometric analysis for elliptic equations on surfaces, A high-order discontinuous Galerkin discretization with multiwavelet-based grid adaptation for compressible flows, Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems, A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes, A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework, Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation, The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations, Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells, A new stable splitting for the isentropic Euler equations, Spectral p-multigrid discontinuous Galerkin solution of the Navier-Stokes equations, On the discontinuous Galerkin computation of N-waves focusing, Hamiltonian-Preserving Discontinuous Galerkin Methods for the Liouville Equation With Discontinuous Potential, A discontinuous Galerkin scheme for the numerical solution of flow problems with discontinuities, Multi-dimensional Optimal Order Detection (MOOD) — a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured Meshes, Discontinuous Galerkin Methods for Linear Problems: An Introduction, Unnamed Item, Automated Parameters for Troubled-Cell Indicators Using Outlier Detection, Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation, Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation, A High-Order Numerical Method for BSPDEs with Applications to Mathematical Finance, A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations, An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative, High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes, A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography, Application of Positivity-Preserving Discontinuous Galerkin Scheme in Gaseous Detonations, An Adaptive Modal Discontinuous Galerkin Finite Element Parallel Method Using Unsplit Multi-Axial Perfectly Matched Layer for Seismic Wave Modeling, A DDG Method with a Residual-Based Artificial Viscosity for the Transonic/Supersonic Compressible Flow, A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation, L$^2$ Error Estimate to Smooth Solutions of High Order Runge--Kutta Discontinuous Galerkin Method for Scalar Nonlinear Conservation Laws with and without Sonic Points, Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes, Convergence of a finite element method for the drift-diffusion semiconductor device equations: the zero diffusion case, On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations, Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations, Fully discrete local discontinuous Galerkin methods for some time-fractional fourth-order problems, Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using P^k elements, Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods, Comparisons of numerical methods with respect to convectively dominated problems, Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations, A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension, Stability analysis and error estimates of local discontinuous Galerkin method for convection-diffusion equations on overlapping mesh with non-periodic boundary conditions, Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, A New High-Order Compact Scheme of Unstructured Finite Volume Method, Hamilton–Jacobi–Bellman Equations, Error Estimate of the Fourth-Order Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Stabilized Cut Discontinuous Galerkin Methods for Advection-Reaction Problems, Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations, A simple shock‐capturing technique for high‐order discontinuous Galerkin methods, Local discontinuous Galerkin methods based on the multisymplectic formulation for two kinds of Hamiltonian PDEs, A γ-DGBGK scheme for compressible multi-fluids, Superconvergence of bi-k Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations, Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes, A Generalization of a Troubled-Cell Indicator to $h$-Adaptive Meshes for Discontinuous Galerkin Methods, An Immersed Discontinuous Galerkin Method for Acoustic Wave Propagation in Inhomogeneous Media, Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes, An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes, Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems, A High-Order Method for Weakly Compressible Flows, Runge-Kutta Central Discontinuous Galerkin Methods for the Special Relativistic Hydrodynamics, A Symmetric Direct Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations, Simulating Magnetohydrodynamic Instabilities with Conservative Perturbed MHD Model Using Discontinuous Galerkin Method, An Energy Conserving Local Discontinuous Galerkin Method for a Nonlinear Variational Wave Equation, High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws, A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation, A Direct ALE Multi-Moment Finite Volume Scheme for the Compressible Euler Equations, Implicit time integration of hyperbolic conservation laws via discontinuous Galerkin methods, Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes, High Order Finite Difference Scheme based on DG Boundary Treatment (FDbDG), Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems, Efficient, Accurate and Energy Stable Discontinuous Galerkin Methods for Phase Field Models of Two-Phase Incompressible Flows, An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation, A Study of Several Artiﬁcial Viscosity Models within the Discontinuous Galerkin Framework, A High Order Central DG method of the Two-Layer Shallow Water Equations, Parameter Identification in Uncertain Scalar Conservation Laws Discretized with the Discontinuous Stochastic Galerkin Scheme, High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes, Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations, AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS, A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems, Unnamed Item, A local discontinuous Galerkin method for nonlinear parabolic SPDEs, A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using K-Means Clustering, A Discontinuous Galerkin Method for Stochastic Conservation Laws, High order explicit local time stepping methods for hyperbolic conservation laws, A discontinuous Galerkin method for the Navier-Stokes equations, Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Method for Hyperbolic Equations Involving $\delta$-Singularities, Numerical Simulation and Experimental Studies of Unsaturated Water Flow in Heterogeneous Systems, High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD, An invariant‐region‐preserving limiter for DG schemes to isentropic Euler equations, High Order Numerical Simulations for the Binary Fluid--Surfactant System Using the Discontinuous Galerkin and Spectral Deferred Correction Methods, Априорные оценки локального разрывного метода Галеркина на разнесенных сетках для решения уравнения параболического типа в рамках однородной задачи Дирихле, Stability analysis and error estimates of arbitrary Lagrangian–Eulerian discontinuous Galerkin method coupled with Runge–Kutta time-marching for linear conservation laws, A High Order Stable Conservative Method for Solving Hyperbolic Conservation Laws on Arbitrarily Distributed Point Clouds, An h-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations, Multiwavelets and Jumps in DG Approximations, A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations, An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws, Optimal error estimates of discontinuous Galerkin methods with generalized fluxes for wave equations on unstructured meshes, Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation, The Runge-Kutta control volume discontinuous finite element method for systems of hyperbolic conservation laws, VALIDATION AND APPLICATION OF AN HIGH-ORDER SPECTRAL DIFFERENCE METHOD FOR FLOW INDUCED NOISE SIMULATION, Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations, High Order Cut Discontinuous Galerkin Methods for Hyperbolic Conservation Laws in One Space Dimension, Central discontinuous Galerkin methods on overlapping meshes for wave equations, Implicit Positivity-Preserving High-Order Discontinuous Galerkin Methods for Conservation Laws, Adaptive multiresolution discontinuous Galerkin schemes for conservation laws, Unnamed Item, High-order mixed weighted compact and non-compact scheme for shock and small length scale interaction, An Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Systems, A conservative high-order discontinuous Galerkin method for the shallow water equations with arbitrary topography, A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes, Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection, NUMERICAL EXPERIMENTS OF THE SPECTRAL VOLUME METHOD FOR VISCOUS FLOWS, Optimal error estimates of the local discontinuous Galerkin methods based on generalized fluxes for 1D linear fifth order partial differential equations, Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise, Extensions of Active Flux to arbitrary order of accuracy, ExaHyPE: an engine for parallel dynamically adaptive simulations of wave problems, Maximum-principle-preserving high-order discontinuous Galerkin methods for incompressible Euler equations on overlapping meshes, A posteriori diffusion analysis of numerical schemes for application to propagating linear waves, An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations, Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems, Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation, Application of the local discontinuous Galerkin method to the solution of the quasi-gas dynamic equation system;Применение локального разрывного метода Галеркина к решению квазигазодинамической системы уравнений, Analysis of the local discontinuous Galerkin method with generalized fluxes for one-dimensional nonlinear convection-diffusion systems, A Well-Balanced Scheme for Euler Equations with Singular Sources, A multi-moment finite volume formulation for the interaction between free surface flow and moving bodies with THINC method, Length-scales for efficient CFL conditions in high-order methods with distorted meshes: application to local-timestepping for \(p\)-multigrid, A robust fifth order finite difference Hermite WENO scheme for compressible Euler equations, Stabilized cut discontinuous Galerkin methods for advection-reaction problems on surfaces, A high-order numerical scheme for stochastic optimal control problem, Moving water equilibria preserving discontinuous Galerkin method for the shallow water equations, An oscillation-free bound-preserving discontinuous Galerkin method for multi-component chemically reacting flows, High-order energy and linear momentum conserving methods for the Klein-Gordon equation, Error analysis of a novel discontinuous Galerkin method for the two-dimensional Poisson's equation, Numerical approximation of living-man steady state solutions for blood flow in arteries using a well-balanced discontinuous Galerkin scheme, High-Order Local Discontinuous Galerkin Method with Multi-Resolution WENO Limiter for Navier-Stokes Equations on Triangular Meshes, A generalized framework for direct discontinuous Galerkin methods for nonlinear diffusion equations, The compact and accuracy preserving limiter for high-order finite volume schemes solving compressible flows, Admissibility preserving subcell limiter for Lax-Wendroff flux reconstruction, An oscillation-free spectral volume method for hyperbolic conservation laws, A collision-based hybrid method for the BGK equation, A superconvergent ultra-weak discontinuous Galerkin method for nonlinear second-order two-point boundary-value problems, A Posteriori Error Analysis for an Ultra-Weak Discontinuous Galerkin Approximations of Nonlinear Second-Order Two-Point Boundary-Value Problems, Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics, The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations, Superconvergence of an Ultra-Weak Discontinuous Galerkin Method for Nonlinear Second-Order Initial-Value Problems, On the conservation property of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations, High-order methods for hypersonic flows with strong shocks and real chemistry, An indicator-based hybrid limiter in discontinuous Galerkin methods for hyperbolic conservation laws, A High Order Positivity-Preserving Discontinuous Galerkin Remapping Method Based on a Moving Mesh Solver for ALE Simulation of the Compressible Fluid Flow, A discontinuous Galerkin finite element model for compound flood simulations, A new troubled cell indicator and a new limiter based on TENO schemes for RKDG methods, Discontinuous Galerkin Methods for Weakly Coupled Hyperbolic MultiDomain Problems, Error self-canceling of a difference scheme maintaining two conservation laws for linear advection equation, New two‐dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes, A discontinuous finite element method for hyperbolic thermal wave problems, Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems, A selective immersed discontinuous Galerkin method for elliptic interface problems, On the computation of steady hopper flows. I: Stress determination for Coulomb materials, Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws, A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods, The discontinuous Galerkin finite element method for the 2D shallow water equations, The discontinuous finite element method for red-and-green light models for the traffic flow, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives, A Review of Parallel Computing in Computational Aeroacoustics, Strong Stability of Explicit Runge--Kutta Time Discretizations, The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations, A Regularized Entropy-Based Moment Method for Kinetic Equations, Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions, Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation, High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations, Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations, A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD, The new discontinuous Galerkin methods based numerical relativity program Nmesh, Three Indication Variables and Their Performance for the Troubled-Cell Indicator using K-Means Clustering

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