Header

UZH-Logo

Maintenance Infos

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.

Statistics

Citations

Dimensions.ai Metrics
6 citations in Web of Science®
3 citations in Scopus®
5 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

1 download since deposited on 29 Nov 2010
1 download since 12 months
Detailed statistics

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:19 Feb 2018 19:59
Publisher:De Gruyter
ISSN:0927-6467
OA Status:Green
Publisher DOI:https://doi.org/10.1515/156939805775122271

Download

Download PDF  'Functional-type a posteriori error estimates for mixed finite element methods'.
Preview
Content: Published Version
Filetype: PDF
Size: 231kB
View at publisher