Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers

DOI10.1016/j.camwa.2021.04.009OpenAlexW3156447148MaRDI QIDQ2027572

Mirjana Brdar, Ljiljana Teofanov, Goran Radojev, Hans-Goerg Roos

Publication date: 27 May 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.05737

zbMATH Keywords

singular perturbationfinite element methodsuperconvergencegraded meshstreamline diffusion methodcharacteristic layers

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)

Related Items

Supercloseness of finite element method for a singularly perturbed convection-diffusion problem on Bakhvalov-type triangular meshes ⋮ The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers

Cites Work

• Unnamed Item
• Unnamed Item
• Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers
• A robust SUPG norm a posteriori error estimator for stationary convection-diffusion equations
• Corner singularities and boundary layers in a simple convection-diffusion problem
• Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers
• Anisotropic interpolation with applications to the finite element method
• On finite difference fitted schemes for singularly perturbed boundary value problems with a parabolic boundary layer
• Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers
• Analysis of the SDFEM for convection-diffusion problems with characteristic layers
• The streamline-diffusion finite element method on graded meshes for a convection-diffusion problem
• Optimal adaptivity for the SUPG finite element method
• Analysis of the SDFEM in a streamline diffusion norm for singularly perturbed convection diffusion problems
• Convergence of local projection stabilisation finite element methods for convection-diffusion problems on layer-adapted meshes
• Interior penalty discontinuous approximations of convection-diffusion problems with parabolic layers
• Finite element approximation of convection diffusion problems using graded meshes
• How accurate is the streamline-diffusion FEM inside characteristic (boundary and interior) layers?
• Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities
• Superconvergence analysis of the Galerkin FEM for a singularly perturbed convection–diffusion problem with characteristic layers
• Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations
• Optimal convergence of basic schemes for elliptic boundary value problems with strong parabolic layers.