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Energy norm a-posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem

by P. Houston and D. Schötzau and Th. Wihler

(Report number 2003-09)

Abstract
In this paper, we develop the a posteriori error estimation of mixed discontinuous Galerkin finite element approximations of the Stokes problem. In particular, computable upper bounds on the error, measured in terms of a natural (mesh-dependent) energy norm, are derived. The proof of the a posteriori error bound is based on rewriting the underlying method in a non-consistent form by introducing appropriate lifting operators, and employing a decomposition result for the discontinuous spaces. A series of numerical experiments highlighting the performance of the proposed a posteriori error estimator on adaptively refined meshes are presented.

Keywords: Discontinuous Galerkin methods, A posteriori error estimation, Stokes problem

@Techreport{HSW03_321,
  author = {P. Houston and D. Sch\"otzau and Th. Wihler},
  title = {Energy norm a-posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-09.pdf },
  year = {2003}
}

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