Convergence of Finite Elements Adapted for Weak Norms

  • We consider finite elements that are adapted to a (semi)norm that is weaker than the one of the trial space. We establish convergence of the finite element solutions to the exact one under the following conditions: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids; the finite element spaces are conforming, nested, and satisfy the inf-sup condition; the error estimator is reliable and appropriately locally efficient; the indicator of a non-marked element is bounded by the estimator contribution associated with the marked elements, and each marked element is subdivided at least once. This abstract convergence result is illustrated by two examples.

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Author:Pedro Morin, Kunibert G. SiebertGND, Andreas Veeser
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-08)
Publishing Institution:Universität Augsburg
Release Date:2007/05/30
Tag:adaptivity; conforming finite elements; convergence
GND-Keyword:Anpassung <Mathematik>; Finite-Elemente-Methode; Konvergenz; Halbnorm
Source:preprint no. 2/2007, Dipartimento di Matematica "F. Enriques''
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik