Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers
Copyright policy )Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers
We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost uniform convergence and superconvergence. The use of graded mesh allows for the SDFEM to prove almost uniform esimates in the SD norm, which is not possible for Shishkin type meshes.
Error bounds for boundary value problems involving PDEs, streamline diffusion method, finite element method, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, superconvergence, Boundary value problems for second-order elliptic equations, graded mesh, FOS: Mathematics, Mathematics - Numerical Analysis, characteristic layers, singular perturbation, Singular perturbations in context of PDEs
Error bounds for boundary value problems involving PDEs, streamline diffusion method, finite element method, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, superconvergence, Boundary value problems for second-order elliptic equations, graded mesh, FOS: Mathematics, Mathematics - Numerical Analysis, characteristic layers, singular perturbation, Singular perturbations in context of PDEs
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