Functional-type a posteriori error estimates for mixed finite element methods
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 ar...
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Published in | Russian journal of numerical analysis and mathematical modelling Vol. 20; no. 4; pp. 365 - 382 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Genthiner Strasse 13 10875 Berlin Germany
Walter de Gruyter
01.01.2005
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Online Access | Get full text |
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Summary: | 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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Bibliography: | istex:83C43B53754F39D0EFE23BC86214451E08C4CA7C 156939805775122271.pdf ark:/67375/QT4-5SJ7TK89-R ArticleID:156939805775122271 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0927-6467 1569-3988 |
DOI: | 10.1515/156939805775122271 |