A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes
Copyright policy )A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes
AbstractWe consider a convection–diffusion problem with Dirichlet boundary conditions posed on a unit square. The problem is discretized using a combination of the standard Galerkin FEM and an h–version of the nonsymmetric discontinuous Galerkin FEM with interior penalties on a layer–adapted mesh with linear/bilinear elements. With specially chosen penalty parameters for edges from the coarse part of the mesh, we prove uniform convergence (in the perturbation parameter) in an associated norm. In the same norm we also establish a supercloseness result. Numerical tests support our theoretical estimates.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
- TU Dresden Germany
- University of Novi Sad Serbia
- Dresden University of Technology
layer-adapted mesh, 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, convection diffusion problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Galerkin finite element method, interior penalty, superconvergence, Boundary value problems for second-order elliptic equations, supercloseness, singular perturbation, Singular perturbations in context of PDEs
layer-adapted mesh, 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, convection diffusion problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Galerkin finite element method, interior penalty, superconvergence, Boundary value problems for second-order elliptic equations, supercloseness, singular perturbation, Singular perturbations in context of PDEs
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