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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
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References:

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