Finite elements on locally uniform meshes for convection-diffusion problems with boundary layers. (English) Zbl 1228.65129
Summary: The layer-adapted meshes used to achieve robust convergence results for problems with layers are not locally uniform. We discuss concepts of almost robust convergence and some realizations of locally-uniform meshes.
MSC:
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
34E15 | Singular perturbations for ordinary differential equations |
65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
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 |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type meshes; locally uniform meshes; layer-adapted meshes; boundary layers; numerical examples; convergenceReferences:
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