Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D. (English) Zbl 1249.65248
The finite element method for the numerical solution of the singularly perturbed linear convection-diffusion problem on Bakhalov-type meshes in 2D is analysed. So far optimal error estimates on Bakhalov-type meshes were only known in the one-dimensional case for this problem. The authors proved (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
Reviewer: Roman Kohut (Ostrava)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
Keywords:
finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type mesh; layer-adapted mesh; optimal error estimates; exponential boundary layersReferences:
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