A posteriori error analysis of an enriched Galerkin method of order one for the Stokes problem

Author:

Girault Vivette1,González María2,Hecht Frédéric1

Affiliation:

1. Laboratoire Jacques-Louis Lions , Sorbonne Universite , Paris , France

2. Departamento de Matematicas and CITIC , Universidade da Coruña , Coruña , Spain

Abstract

Abstract We derive optimal reliability and efficiency of a posteriori error estimates for the steady Stokes problem, with a nonhomogeneous Dirichlet boundary condition, solved by a stable enriched Galerkin scheme (EG) of order one on triangular or quadrilateral meshes in ℝ2, and tetrahedral or hexahedral meshes in ℝ3.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics

Reference34 articles.

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2. M. Ainsworth and J. Oden, A posteriori error estimators for the Stokes and Oseen equations, SIAM J. Numer. Anal., 34 (1997), pp. 228-245.

3. A. Allendes, E. Otarola, and A. Salgado, A posteriori error estimates for the Stokes problem with singular sources, Comput. Methods Appl. Mech. Engrg., 345 (2019), pp. 1007-1032.

4. R. Bank and B. Welfert, A posteriori error estimates for the Stokes prob lem, SIAM J. Numer. Anal., 28 (1991), pp. 591-623.

5. R. Becker, E. Burman, P. Hansbo, and M. Larson, A reduced ?1-Discontinuous Galerkin Method, tech. rep., Chalmers Finite Element Centre, Chalmers University of Technology, 2003.

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