Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
From MaRDI portal
Publication:4653880
DOI10.1137/S0036142902404182zbMath1078.65080OpenAlexW1994099903MaRDI QIDQ4653880
Publication date: 1 March 2005
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036142902404182
error estimatesconservation lawsfinite elementtotal variation diminishing Runge-Kutta methoddicontinuous Galerkin method
Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Related Items
An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations, Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation, A discontinuous Galerkin method for the Camassa‐Holm‐Kadomtsev‐Petviashvili type equations, Implicit-Explicit Time Discretization for Oseen’s Equation at High Reynolds Number with Application to Fractional Step Methods, A high-order numerical scheme for stochastic optimal control problem, Stabilizing discontinuous Galerkin methods using Dafermos' entropy rate criterion. I: One-dimensional conservation laws, Uniform stability for local discontinuous Galerkin methods with implicit-explicit Runge-Kutta time discretizations for linear convection-diffusion equation, Exponential DG methods for Vlasov equations, Discontinuous Galerkin method based on the reduced space for the nonlinear convection-diffusion-reaction equation, Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws, Stability of structure-aware Taylor methods for tents, A conservative discontinuous Galerkin discretization for the chemically reacting Navier-Stokes equations, Negative norm estimates for arbitrary Lagrangian-Eulerian discontinuous Galerkin method for nonlinear hyperbolic equations, 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, A priori error estimates of Adams-Bashforth discontinuous Galerkin methods for scalar nonlinear conservation laws, Stability analysis and error estimates of semi-implicit spectral deferred correction coupled with local discontinuous Galerkin method for linear convection-diffusion equations, Analysis of the local discontinuous Galerkin method for the drift-diffusion model of semiconductor devices, Error analysis of the semi-discrete local discontinuous Galerkin method for compressible miscible displacement problem in porous media, A discontinuous Galerkin method for blood flow and solute transport in one-dimensional vessel networks, Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for KdV type equations, Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions, Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty, Finite element error estimates for nonlinear convective problems, Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems, 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, Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations, Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model, Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation, Local discontinuous Galerkin method for the Keller-Segel chemotaxis model, Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models, Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using Pk elements, Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods, Negative-order norm estimates for nonlinear hyperbolic conservation laws, A fully-discrete local discontinuous Galerkin method for convection-dominated Sobolev equation, Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows, Discontinuous Galerkin Methods for Weakly Coupled Hyperbolic MultiDomain Problems, Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws: Analysis and application in one dimension, Local discontinuous Galerkin method for incompressible miscible displacement problem in porous media, Error estimates to smooth solutions of semi‐discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws, Third-order explicit Runge-Kutta discontinuous Galerkin method for linear conservation law with inflow boundary condition, Supercloseness of weak Galerkin method on Bakhvalov-type mesh for a singularly perturbed problem in 1D, Dispersion and dissipation errors of two fully discrete discontinuous Galerkin methods, A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model, Error Estimate of the Fourth-Order Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws on moving simplex meshes, $hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Navier--Stokes Equations, Discontinuous Galerkin methods with nodal and hybrid modal/nodal triangular, quadrilateral, and polygonal elements for nonlinear shallow water flow, A weak Galerkin finite element method for nonlinear conservation laws, Local discontinuous Galerkin methods to a dispersive system of KdV-type equations, Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates, Error estimates for the third order explicit Runge-Kutta discontinuous Galerkin method for a linear hyperbolic equation in one-dimension with discontinuous initial data, Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems, Optimal error estimate of the local discontinuous Galerkin methods based on the generalized alternating numerical fluxes for nonlinear convection-diffusion equations, Local discontinuous Galerkin method with implicit-explicit time marching for incompressible miscible displacement problem in porous media, Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems, Stability and convergence of a local discontinuous Galerkin finite element method for the general Lax equation, A discontinuous Galerkin-front tracking scheme and its optimal-optimal error estimation, A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems, Error estimates for higher-order finite volume schemes for convection-diffusion problems, Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system, DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM, Superconvergence and time evolution of discontinuous Galerkin finite element solutions, Central Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation, Dissipative and Conservative Local Discontinuous Galerkin Methods for the Fornberg-Whitham Type Equations, Analysis of discontinuous Galerkin methods with upwind-biased fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients, Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems, Fourier analysis for discontinuous Galerkin and related methods, A discontinuous Galerkin method with Lagrange multiplier for hyperbolic conservation laws with boundary conditions, The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations, Stability Analysis of Discontinuous Galerkin Discrete Shock Profiles for Steady Scalar Conservation Laws, A review of a posteriori error control and adaptivity for approximations of non‐linear conservation laws, Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives, Asymptotically exact posteriori error estimates for the local discontinuous Galerkin method applied to nonlinear convection-diffusion problems, Error estimates for the standard Galerkin-finite element method for the shallow water equations, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations, Artificial boundary layers in discontinuous Galerkin solutions to shallow water equations in channels, A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals, A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes, Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger-type equations, A Discontinuous Galerkin Method for Stochastic Conservation Laws, Implicit-explicit local discontinuous Galerkin methods with generalized alternating numerical fluxes for convection-diffusion problems, Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation, Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations, Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Method for Hyperbolic Equations Involving $\delta$-Singularities, Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs, An ultra-weak discontinuous Galerkin method with implicit-explicit time-marching for generalized stochastic KdV equations, Arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for linear convection-diffusion equations, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems, 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, Local discontinuous Galerkin methods for the \(\mu \)-Camassa-Holm and \(\mu \)-Degasperis-Procesi equations, Error estimates of Runge–Kutta discontinuous galerkin methods for the Vlasov–Maxwell system, A Sparse Grid Discontinuous Galerkin Method for High-Dimensional Transport Equations and Its Application to Kinetic Simulations, The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Error boundedness of discontinuous Galerkin methods with variable coefficients, Superconvergence of Arbitrary Lagrangian--Eulerian Discontinuous Galerkin Methods for Linear Hyperbolic Equations, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations, A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface, Accuracy-enhancement of discontinuous Galerkin solutions for convection-diffusion equations in multiple-dimensions, Local discontinuous Galerkin method for nonlinear time-space fractional subdiffusion/superdiffusion equations, Weighted error estimates for transient transport problems discretized using continuous finite elements with interior penalty stabilization on the gradient jumps, Superconvergence analysis of the Runge-Kutta discontinuous Galerkin methods for a linear hyperbolic equation, A Posteriori Analysis of Discontinuous Galerkin Schemes for Systems of Hyperbolic Conservation Laws, Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations, 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, Local analysis of local discontinuous Galerkin method for the time-dependent singularly perturbed problem, Convergence analysis of some tent-based schemes for linear hyperbolic systems