Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection – diffusion – reaction problems

DOI10.1080/00207160.2023.2166347zbMath1524.65858MaRDI QIDQ6106724

Ali Sendur, Gautam B. Singh, Srinivasan Natesan

Publication date: 3 July 2023

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

zbMATH Keywords

convection-diffusion problemsuperconvergenceShishkin meshdiscontinuous Galerkin method with interior penaltysingularly perturbed 2D elliptic BVPs

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05)

Cites Work

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• Discontinuous Galerkin methods with interior penalties on graded meshes for 2D singularly perturbed convection-diffusion problems
• Analysis of the DGFEM for nonlinear convection-diffusion problems
• Superconvergence of discontinuous Galerkin method with interior penalties for singularly perturbed two-point boundary-value problems
• Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator
• Analysis of the discontinuous Galerkin method for nonlinear convection--diffusion problems
• Interior penalty discontinuous approximations of convection-diffusion problems with parabolic layers
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• OptimalL^∞(L²)-Error Estimates for the DG Method Applied to Nonlinear Convection–Diffusion Problems with Nonlinear Diffusion
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems
• A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

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