The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case

DOI10.2307/2008501zbMath0695.65066OpenAlexW4238285603MaRDI QIDQ3471667

Chi-Wang Shu, Suchung Hou, Bernardo Cockburn

Publication date: 1990

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: http://purl.umn.edu/4982

zbMATH Keywords

numerical resultsconservation lawsmaximum principlestwo-dimensionalgeneral triangulationsRunge-Kutta local projection discontinuous Galerkin methods

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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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, A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids, 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, A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation, Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes, Reconstructed Discontinuous Galerkin Methods for Hyperbolic Diffusion Equations on Unstructured Grids, 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, High-Order Runge-Kutta Discontinuous Galerkin Methods with a New Type of Multi-Resolution WENO Limiters on Tetrahedral Meshes, A selective immersed discontinuous Galerkin method for elliptic interface problems, On a Cell Entropy Inequality for Discontinuous Galerkin Methods, On adaptive timestepping for weakly instationary solutions of hyperbolic conservation laws via adjoint error control, An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model, Pointwise error estimates of the local discontinuous Galerkin method for a second order elliptic problem, An Error Estimate for Finite Volume Methods for Multidimensional Conservation Laws, A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives, Unnamed Item, A Provably Positive Discontinuous Galerkin Method for Multidimensional Ideal Magnetohydrodynamics, 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, 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 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, High‐order accuratep‐multigrid discontinuous Galerkin solution of the Euler equations, Stability analysis and error estimates of arbitrary Lagrangian–Eulerian discontinuous Galerkin method coupled with Runge–Kutta time-marching for linear conservation laws, Local error estimates of mixed discontinuous Galerkin methods for elliptic problems, An h-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations, Strong Stability of Explicit Runge--Kutta Time Discretizations, The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Superconvergence of Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic 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, Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions, Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations, Numerical Solution of the Viscous Surface Wave with Discontinuous Galerkin Method, Analysis of a high-order space and time discontinuous Galerkin method for elastodynamic equations. Application to 3D wave propagation, An upwinding mixed finite element method for a mean field model of superconducting vortices, High Order Cut Discontinuous Galerkin Methods for Hyperbolic Conservation Laws in One Space Dimension, Central discontinuous Galerkin methods on overlapping meshes for wave equations, High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations, Implicit Positivity-Preserving High-Order Discontinuous Galerkin Methods for Conservation Laws, Unnamed Item, Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations, An Essentially Oscillation-Free Discontinuous Galerkin Method for Hyperbolic Systems, NUMERICAL COUPLING OF TWO SCALAR CONSERVATION LAWS BY A RKDG METHOD, Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions, Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes, Convergence of higer order finite volume schemes on irregular grids, A finite volume multi-moment method with boundary variation diminishing principle for Euler equation on three-dimensional hybrid unstructured grids, A high-order nodal discontinuous Galerkin method for solution of compressible non-cavitating and cavitating flows, A new vertex-based limiting approach for nodal discontinuous Galerkin methods on arbitrary unstructured meshes, A Lagrangian discontinuous Galerkin hydrodynamic method, Semi-implicit staggered discontinuous Galerkin schemes for axially symmetric viscous compressible flows in elastic tubes, A reconstructed direct discontinuous Galerkin method for simulating the compressible laminar and turbulent flows on hybrid grids, Galerkin methods for Boltzmann-Poisson transport with reflection conditions on rough boundaries, The discontinuous Galerkin spectral element methods for compressible flows on two-dimensional mixed grids, Approximate Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws, Predictor-corrector LU-SGS discontinuous Galerkin finite element method for conservation laws, A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws, A \(p\)-adaptive local discontinuous Galerkin level set method for Willmore flow, A direct discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids, A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows, A nonlinear filter for high-order discontinuous Galerkin discretizations with discontinuity resolution within the cell, A reconstructed discontinuous Galerkin method for magnetohydrodynamics on arbitrary grids, Superconvergence of local discontinuous Galerkin methods for partial differential equations with higher order derivatives, Efficient implementation of smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, A curved-element unstructured discontinuous Galerkin method on GPUs for the Euler equations, Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers, Positivity-preserving high-order discontinuous Galerkin schemes for ten-moment Gaussian closure equations, A high order conservative semi-Lagrangian discontinuous Galerkin method for two-dimensional transport simulations, Local discontinuous Galerkin method for the Keller-Segel chemotaxis model, A direct flux reconstruction scheme for advection-diffusion problems on triangular grids, Superconvergence of local discontinuous Galerkin method for one-dimensional linear Schrödinger equations, A Riemann problem based method for solving compressible and incompressible flows, An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction, Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes, Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws, Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics, Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes, Positivity-preserving discontinuous Galerkin methods with Lax-Wendroff time discretizations, Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods, WENO schemes and their application as limiters for RKDG methods based on trigonometric approximation spaces, High-order local discontinuous Galerkin method for simulating wormhole propagation, Hybrid weighted essentially non-oscillatory schemes with different indicators, Element centered smooth artificial viscosity in discontinuous Galerkin method for propagation of acoustic shock waves on unstructured meshes, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes, Exponential boundary-layer approximation space for solving the compressible laminar Navier-Stokes equations, Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method, Stability analysis and error estimates of local discontinuous Galerkin methods with semi-implicit spectral deferred correction time-marching for the Allen-Cahn equation, High-order discontinuous Galerkin methods for coastal hydrodynamics applications, Implicit large eddy simulation of compressible turbulence flow with \(\mathrm{P}_n\mathrm{T}_m-\mathrm{BVD}\) scheme, Local discontinuous Galerkin methods for the Boussinesq coupled BBM system, The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law, Analysis of discontinuous Galerkin methods with upwind-biased fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients, Energy dissipative local discontinuous Galerkin methods for Keller-Segel chemotaxis model, Smooth and compactly supported viscous sub-cell shock capturing for discontinuous Galerkin methods, A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations, Maximum-principle-preserving third-order local discontinuous Galerkin method for convection-diffusion equations on overlapping meshes, An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics, A simple, high-order and compact WENO limiter for RKDG method, Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids, A high order scheme for unsteady heat conduction equations, Stability analysis and error estimates of local discontinuous Galerkin methods for convection-diffusion equations on overlapping meshes, Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case, A novel solver for the generalized Riemann problem based on a simplified LeFloch-Raviart expansion and a local space-time discontinuous Galerkin formulation, Implicit multistage two-derivative discontinuous Galerkin schemes for viscous conservation laws, A high-order vertex-centered quasi-Lagrangian discontinuous Galerkin method for compressible Euler equations in two-dimensions, Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations, Local discontinuous Galerkin methods for nonlinear Schrödinger equations, Stabilizing radial basis function methods for conservation laws using weakly enforced boundary conditions, On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems, \(P_0\) time/space subcell limiting DG-DGLM method for hyperbolic systems of conservation laws, Local-maximum-and-minimum-preserving solution remapping technique to accelerate flow convergence for discontinuous Galerkin methods in shape optimization design, High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems, A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux, A limiting approach for DG discretizations on mixed type meshes, On discrete maximum principles for discontinuous Galerkin methods, Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations, Adaptive direct discontinuous Galerkin method for elliptic equations, On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows, Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations, A rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions, A new discontinuous Galerkin method for elastic waves with physically motivated numerical fluxes, Positivity-preserving well-balanced arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the shallow water equations, Superconvergence analysis of the ultra-weak local discontinuous Galerkin method for one dimensional linear fifth order equations, Arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for linear convection-diffusion equations, A third-order weighted variational reconstructed discontinuous Galerkin method for solving incompressible flows, Maximum principle and positivity-preserving high order spectral volume schemes with parametrized flux limiters for solving hyperbolic conservation laws, A discontinuous Galerkin ALE method for compressible viscous flows in moving domains, A quasi-conservative discontinuous Galerkin method for multi-component flows using the non-oscillatory kinetic flux. II: ALE framework, An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density, High order modal discontinuous Galerkin implicit-explicit Runge Kutta and linear multistep schemes for the Boltzmann model on general polygonal meshes, A stable discontinuous Galerkin method for linear elastodynamics in 3D geometrically complex elastic solids using physics based numerical fluxes, A novel staggered semi-implicit space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations, Enforcing strong stability of explicit Runge-Kutta methods with superviscosity, Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws, Compact multi-stage reconstruction method on polyhedral unstructured grids: extension to higher-order finite volume scheme, Error estimates of the local discontinuous Galerkin methods for two-dimensional \((\mu)\)-Camassa-Holm equations, Local discontinuous Galerkin methods for diffusive-viscous wave equations, A fractional-step DG-FE method for the time-dependent generalized Boussinesq equations, Simulation of a viscous compressible flow past a circular cylinder with high-order discontinuous Galerkin methods, Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations, Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. II: Efficient flux quadrature., Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. I: General formulation., Optimal, globally constraint-preserving, \(\mathrm{DG(TD)}^2\) schemes for computational electrodynamics based on two-derivative Runge-Kutta timestepping and multidimensional generalized Riemann problem solvers -- a von Neumann stability analysis, An improved WENO method based on Gauss-kriging reconstruction with an optimized hyper-parameter, Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure, A neural network based shock detection and localization approach for discontinuous Galerkin methods, Arbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume method, An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations, A wavelet-free approach for multiresolution-based grid adaptation for conservation laws, The direct discontinuous Galerkin methods with implicit-explicit Runge-Kutta time marching for linear convection-diffusion problems, Superconvergence analysis of the Runge-Kutta discontinuous Galerkin method with upwind-biased numerical flux for two-dimensional linear hyperbolic equation, Maximum-principle-preserving local discontinuous Galerkin methods for Allen-Cahn equations, A reconstructed discontinuous Galerkin method for incompressible flows on arbitrary grids, On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: energy conservation and multi-symplecticity, Weighted essentially non-oscillatory stochastic Galerkin approximation for hyperbolic conservation laws, Low-dissipation BVD schemes for single and multi-phase compressible flows on unstructured grids, Optimized filters for stabilizing high-order large eddy simulation, An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions, A characteristic-featured shock wave indicator on unstructured grids based on training an artificial neuron, An implicit high-order \(k\)-exact finite-volume approach on vertex-centered unstructured grids for incompressible flows, A horizontally explicit, vertically implicit (HEVI) discontinuous Galerkin scheme for the 2-dimensional Euler and Navier-Stokes equations using terrain-following coordinates, High order entropy stable and positivity-preserving discontinuous Galerkin method for the nonlocal electron heat transport model, A coupled discontinuous Galerkin-finite volume framework for solving gas dynamics over embedded geometries, Performance and accuracy of hybridized flux reconstruction schemes, Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise, Local discontinuous Galerkin methods for the \(abcd\) nonlinear Boussinesq system, Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for KdV type equations, HHO methods for the incompressible Navier-Stokes and the incompressible Euler equations, A class of high-order weighted compact central schemes for solving hyperbolic conservation laws, High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations, An improved simple WENO limiter for discontinuous Galerkin methods solving hyperbolic systems on unstructured meshes, A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation, A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property, How to design a generic accuracy-enhancing filter for discontinuous Galerkin methods, \(p\)-multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation, Von Neumann stability analysis of DG-like and P\(N\)P\(M\)-like schemes for PDEs with globally curl-preserving evolution of vector fields, Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin-Bona-Mahony equation, Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation, A characteristic-featured shock wave indicator for conservation laws based on training an artificial neuron, Application of discontinuous Galerkin method in supersonic and hypersonic gas flows, High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves, An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form, Implicit method and slope limiter in AHMR procedure for high order discontinuous Galerkin methods for compressible flows, Numerical analysis of the unconditionally stable discontinuous Galerkin schemes for the nonstationary conduction-convection problem, Stochastic discontinuous Galerkin methods (SDGM) based on fluctuation-dissipation balance, A direct discontinuous Galerkin method for the incompressible Navier-Stokes equations on arbitrary grids, Optimal Runge-Kutta schemes for pseudo time-stepping with high-order unstructured methods, A high-order Lagrangian discontinuous Galerkin hydrodynamic method for quadratic cells using a subcell mesh stabilization scheme, Spectral properties of high-order element types for implicit large eddy simulation, \textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction, Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity, A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations, An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes, High-order multi-moment finite volume method with smoothness adaptive fitting reconstruction for compressible viscous flow, Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation, Bounded and compact weighted essentially nonoscillatory limiters for discontinuous Galerkin schemes: triangular elements, Compact high order finite volume method on unstructured grids. IV: Explicit multi-step reconstruction schemes on compact stencil, A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws, High order positivity-preserving discontinuous Galerkin schemes for radiative transfer equations on triangular meshes, A coupled implicit-explicit time integration method for compressible unsteady flows, A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property, Assessment of aeroacoustic resolution properties of DG schemes and comparison with DRP schemes, On the effect of temporal error in high-order simulations of unsteady flows, A new WENO based Chebyshev spectral volume method for solving one- and two-dimensional conservation laws, A robust CFL condition for the discontinuous Galerkin method on triangular meshes, High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters, A hybrid Hermite WENO scheme for hyperbolic conservation laws, A discontinuous Galerkin method for the Aw-Rascle traffic flow model on networks, Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form, A high-order space-time ultra-weak discontinuous Galerkin method for the second-order wave equation in one space dimension, A new WENO weak Galerkin finite element method for time dependent hyperbolic equations, Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations, High-order methods for simulations in engineering, Time step restrictions for strong-stability-preserving multistep Runge-Kutta discontinuous Galerkin methods, A new ADER discontinuous Galerkin method based on differential transformation procedure for hyperbolic conservation laws, An efficient high-order least square-based finite difference-finite volume method for solution of compressible Navier-Stokes equations on unstructured grids, Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation, High-order numerical simulation of axisymmetric wave phase conjugation, Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations, A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems, Well-balanced discontinuous Galerkin method for shallow water equations with constant subtraction techniques on unstructured meshes, Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points, An \(h-\) adaptive local discontinuous Galerkin method for simulating wormhole propagation with Darcy-Forcheiner model, Entropy-stable, high-order summation-by-parts discretizations without interface penalties, An ultra-weak discontinuous Galerkin method with implicit-explicit time-marching for generalized stochastic KdV equations, Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine, Optimal error estimates of the discontinuous Galerkin method with upwind-biased fluxes for 2D linear variable coefficients hyperbolic equations, Development of a multiscale LES model in the context of a modal discontinuous Galerkin method, On the behaviour of fully-discrete flux reconstruction schemes, Semi-implicit discontinuous Galerkin methods for the incompressible Navier-Stokes equations on adaptive staggered Cartesian grids, Von Neumann stability analysis of globally constraint-preserving DGTD and PNPM schemes for the Maxwell equations using multidimensional Riemann solvers, Lagrangian discontinuous Galerkin hydrodynamic methods in axisymmetric coordinates, Analysis of slope limiters on unstructured triangular meshes, A discontinuous Galerkin fast spectral method for the full Boltzmann equation with general collision kernels, A high-order and interface-preserving discontinuous Galerkin method for level-set reinitialization, Superconvergence analysis of local discontinuous Galerkin methods for linear convection-diffusion equations in one space dimension, Fourier analysis of local discontinuous Galerkin methods for linear parabolic equations on overlapping meshes, A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem, Discontinuous mixed covolume methods for linear parabolic integrodifferential problems, A novel high-order solver for simulation of incompressible flows using the flux reconstruction method and lattice Boltzmann flux solver, A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows, Local error estimates for Runge-Kutta discontinuous Galerkin methods with upwind-biased numerical fluxes for a linear hyperbolic equation in one-dimension with discontinuous initial data, 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, Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise, 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, 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, Analysis of the local discontinuous Galerkin method with generalized fluxes for one-dimensional nonlinear convection-diffusion systems, A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations, A robust fifth order finite difference Hermite WENO scheme for compressible Euler equations, A sub-element adaptive shock capturing approach for discontinuous Galerkin methods, Stabilized cut discontinuous Galerkin methods for advection-reaction problems on surfaces, A high-order numerical scheme for stochastic optimal control problem, A high-order entropically-damped artificial compressibility approach on moving and deforming domains, Moving water equilibria preserving discontinuous Galerkin method for the shallow water equations, Development of a gyrokinetic hyperbolic solver based on discontinuous Galerkin method in tokamak geometry, High-fidelity simulations for Turing pattern formation in multi-dimensional Gray-Scott reaction-diffusion system, Error analysis of a novel discontinuous Galerkin method for the two-dimensional Poisson's equation, 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, Investigation of the efficiency of using numerical schemes of a high order of accuracy for solving Navier-Stokes and Reynolds equations on unstructured adapted grids, An oscillation-free spectral volume method for hyperbolic conservation laws, Spatio‐temporal scalar auxiliary variable approach for the nonlinear convection–diffusion equation with discontinuous Galerkin method, A high-order cross-platform incompressible Navier-Stokes solver via artificial compressibility with application to a turbulent jet, Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics, 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, On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics, An indicator-based hybrid limiter in discontinuous Galerkin methods for hyperbolic conservation laws, A new troubled cell indicator and a new limiter based on TENO schemes for RKDG methods, Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws, A summary of numerical methods for time-dependent advection-dominated partial differential equations, A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods, The discontinuous Galerkin finite element method for the 2D shallow water equations, An edge-based stabilized finite element method for solving compressible flows: formulation and parallel implementation., 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