title: A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations
creator: Buß, Hinderk Martens
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 2003
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/3992/1/thesis_23_01_01.pdf
identifier: DOI:10.11588/heidok.00003992
identifier: urn:nbn:de:bsz:16-opus-39926
identifier:   Buß, Hinderk Martens  (2003) A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/3992/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng