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Residual type a posteriori error estimates for upwinding finite volume approximations of elliptic
 

Summary: Residual type a posteriori error estimates for
upwinding finite volume approximations of elliptic
boundary value problems
Lutz Angermann
Abstract: This article describes the extension of recent methods for a posteriori error
control such as dual-weighted residual methods to node-centered finite volume dis-
cretizations of second order elliptic boundary value problems with upwinding.
Keywords: Finite volume methods, a posteriori error control, DWR method
2010 Mathematics Subject Classification: 65 N 08, 65 N 15, 65 N 30, 65 N 50
1 Introduction
In this paper, we give a short overview on recent a posteriori error estimates
for node-centered finite volume discretizations of second-order elliptic PDEs in
d {2, 3} independent variables.
Since finite volume methods do not possess, in general, the so-called Galerkin-
orthogonality property, special attention is paid to the treatment of the resulting
defect term. It is shown that the extension of both the classical residual a
posteriori error estimates as well as the more recent dual-weighted a posteriori
error estimates to finite volume discretizations is possible in a reasonable way.
We consider mainly Voronoi and Donald finite volume partitions on simplicial
primary partitions of the domain, however the ideas can be extendend to more

  

Source: Angermann, Lutz - Institut für Mathematik, Technische Universität Clausthal

 

Collections: Mathematics