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A posteriori error analysis for elliptic PDEs on domains with complicated structures


Carstensen, C; Sauter, S (2004). A posteriori error analysis for elliptic PDEs on domains with complicated structures. Numerische Mathematik, 96(4):691-721.

Abstract

The discretisation of boundary value problems on complicated domains cannot resolve all geometric details such as small holes or pores. The model problem of this paper consists of a triangulated polygonal domain with holes of a size of the mesh-width at most and mixed boundary conditions for the Poisson equation. Reliable and efficient a posteriori error estimates are presented for a fully numerical discretisation with conforming piecewise affine finite elements. Emphasis is on technical difficulties with the numerical approximation of the domain and their influence on the constants in the reliability and efficiency estimates.

The discretisation of boundary value problems on complicated domains cannot resolve all geometric details such as small holes or pores. The model problem of this paper consists of a triangulated polygonal domain with holes of a size of the mesh-width at most and mixed boundary conditions for the Poisson equation. Reliable and efficient a posteriori error estimates are presented for a fully numerical discretisation with conforming piecewise affine finite elements. Emphasis is on technical difficulties with the numerical approximation of the domain and their influence on the constants in the reliability and efficiency estimates.

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8 citations in Web of Science®
5 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
Uncontrolled Keywords:Poisson problem; mixed boundary conditions; complicated domains; extension operators; trace theorems; Poincare inequalities; conforming piecewise affine elements; a posteriori error estimations; finite element method; boundary value problem
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISSN:0029-599X
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00211-003-0495-4
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1049.65120
Permanent URL: https://doi.org/10.5167/uzh-21775

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