A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations

A theoretical framework is presented within which we can systematically develop a posteriori error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory can also cover constrained variational formulations. Two applications are discussed in detail: the Dirichlet Problem and the Obstacle Problem. A number of technical issues is considered, which pertain to the evaluation of the proposed error bounds using finite element methods: Inter alia a novel non-conforming discretisation scheme for the dual formulation is analysed. The resulting algebraic problem may be solved by a new preconditioned relaxation method, for which a proof of convergence is supplied.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2003

Author dc:creator

• Buß, Hinderk Martens

Contributors dc:contributor

• Rannacher, Rolf

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/3992

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:3992