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

Carstensen, Carsten ; Sauter, Stefan A.

In: Numerische Mathematik, 2004, vol. 96, no. 4, p. 691-721

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    Titre
    • A posteriori error analysis for elliptic pdes on domains with complicated structures
    Auteur
    • Carstensen, Carsten. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria
    • Sauter, Stefan A.. Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, 8057, Zürich, Switzerland
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319745
    Summary
    Summary.: 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