Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D.

DOI10.1007/s10492-012-0007-xzbMath1249.65248OpenAlexW2005280306MaRDI QIDQ434488

Martin Schopf, Hans-Goerg Roos

Publication date: 10 July 2012

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

Full work available at URL: https://eudml.org/doc/247053

zbMATH Keywords

singular perturbationfinite element methodconvection-diffusion problemoptimal error estimateslayer-adapted meshexponential boundary layersBakhvalov-type mesh

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) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (7)

The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems ⋮ Improved localized radial basis functions with fitting factor for dominated convection-diffusion differential equations ⋮ Supercloseness of finite element method for a singularly perturbed convection-diffusion problem on Bakhvalov-type triangular meshes ⋮ Convergence of a finite element method on a Bakhvalov‐type mesh for a singularly perturbed convection–diffusion equation in <scp>2D</scp> ⋮ Error estimate of BDF2 scheme on a Bakhvalov-type mesh for a singularly perturbed Volterra integro-differential equation ⋮ Uniform convergence of finite element method on Bakhvalov-type triangular mesh for a singularly perturbed problem featuring exponential layers ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012

Cites Work

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• Error estimates for linear finite elements on Bakhvalov-type meshes.
• A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem
• A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes
• A technique to prove parameter-uniform convergence for a singularly perturbed convection-diffusion equation
• The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy
• Uniform superconvergence of a Galerkin finite element method on Shishkin-type meshes
• Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem
• Layer-adapted meshes for one-dimensional reaction–convection–diffusion problems
• Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem

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