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A supercloseness result for the discontinuous Galerkin stabilization of convection–diffusion problems on Shishkin meshes
Author(s) -
Roos HansGörg,
Zarin Helena
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20241
Subject(s) - discontinuous galerkin method , mathematics , finite element method , discretization , polygon mesh , galerkin method , convection–diffusion equation , bilinear form , norm (philosophy) , unit square , dirichlet boundary condition , bilinear interpolation , partial differential equation , mathematical analysis , boundary value problem , geometry , statistics , physics , political science , law , thermodynamics
Abstract We 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