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Anisotropic a posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem
Author(s) -
Creusé Emmanuel,
Nicaise Serge
Publication year - 2006
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.20107
Subject(s) - polygon mesh , estimator , mathematics , isotropy , upper and lower bounds , anisotropy , a priori and a posteriori , galerkin method , finite element method , discontinuous galerkin method , approximation error , mathematical analysis , geometry , physics , philosophy , statistics , epistemology , quantum mechanics , thermodynamics
This article presents a posteriori error estimates for the mixed discontinuous Galerkin approximation of the stationary Stokes problem. We consider anisotropic finite element discretizations, i.e., elements with very large aspect ratio. Our analysis covers two‐ and three‐dimensional domains. Lower and upper error bounds are proved with minimal assumptions on the meshes. The lower error bound is uniform with respect to the mesh anisotropy. The upper error bound depends on a proper alignment of the anisotropy of the mesh, which is a common feature of anisotropic error estimation. In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally. The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimator. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006