An optimal-order \(L^2\)-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions

DOI10.1016/j.cma.2009.02.006zbMath1227.65085OpenAlexW2161505591MaRDI QIDQ649478

Kaixin Wang, Shuyu Sun, Hong Wang, Mary Fanett Wheeler

Publication date: 30 November 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2009.02.006

zbMATH Keywords

convergence analysiserror estimatessuperconvergencediscontinuous Galerkin methodsIIPGNIPG

Mathematics Subject Classification ID

Diffusion (76R50) 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)

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Cites Work

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• Compatible algorithms for coupled flow and transport
• Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case
• A discontinuous \(hp\) finite element method for diffusion problems
• Discontinuous Galerkin methods for coupled flow and reactive transport problems
• Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport
• Stabilized hp-DGFEM for Incompressible Flow
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates
• Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems
• Discontinuous Galerkin Method for Modeling Flow and Reactive Transport in Porous Media
• Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media