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Functional-type a posteriori error estimates for mixed finite element methods


Repin, S; Smolianski, A (2005). Functional-type a posteriori error estimates for mixed finite element methods. Russian Journal of Numerical Analysis and Mathematical Modelling, 20(4):365-382.

Abstract

This paper concerns a posteriori error estimation for the primal and dual mixed finite element methods applied to the diffusion problem. The problem is considered in a general setting with inhomogeneous mixed Dirichlet–Neumann boundary conditions. New functional-type a posteriori error estimators are proposed that exhibit the ability both to indicate the local error distribution and to ensure upper bounds for discretization errors in primal and dual (flux) variables. The latter property is a direct consequence of the absence in the estimators of any mesh-dependent constants; the only constants present in the estimates stem from the Friedrichs and trace inequalities and, thus, are global and dependent solely on the domain geometry and the bounds of the diffusion matrix. The estimators are computationally cheap and require only the projections of piecewise constant functions onto the spaces of the lowest-order Raviart–Thomas or continuous piecewise linear elements. It is shown how these projections can be easily realized by simple local averaging.

Abstract

This paper concerns a posteriori error estimation for the primal and dual mixed finite element methods applied to the diffusion problem. The problem is considered in a general setting with inhomogeneous mixed Dirichlet–Neumann boundary conditions. New functional-type a posteriori error estimators are proposed that exhibit the ability both to indicate the local error distribution and to ensure upper bounds for discretization errors in primal and dual (flux) variables. The latter property is a direct consequence of the absence in the estimators of any mesh-dependent constants; the only constants present in the estimates stem from the Friedrichs and trace inequalities and, thus, are global and dependent solely on the domain geometry and the bounds of the diffusion matrix. The estimators are computationally cheap and require only the projections of piecewise constant functions onto the spaces of the lowest-order Raviart–Thomas or continuous piecewise linear elements. It is shown how these projections can be easily realized by simple local averaging.

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6 citations in Web of Science®
2 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:De Gruyter
ISSN:0927-6467
Publisher DOI:https://doi.org/10.1515/156939805775122271
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2161108
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1086.65103

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