title: Duality-based adaptivity of model and discretization in multiscale finite-element methods
creator: Maier, Matthias Sebastian
subject: ddc-510
subject: 510 Mathematics
description: This thesis develops strategies for a posteriori error control of discretization and model errors, as well as adaptation strategies, in the context of multiscale finite-element methods. This is done within the general methodology  of the DualWeighted Residual Method (DWR).  In particular, a reformulation of the Heterogeneous Multiscale Method(HMM) as an abstract model-adaptation framework is introduced that explicitly decouples discretization and model parameters. Based on the framework a samplingadaptation strategy is proposed that allows for simultaneous control of discretization and model errors with the help of classical refinement strategies for mesh and sampling regions. Further, a model-adaptation approach is derived that interprets model adaptivity as a minimization problem of a local model-error indicator.    This allows for the formulation of an efficient post-processing strategy that lifts the requirement of strict a priori knowledge about applicability and quality of  effective models. The proposed framework is tested on an elliptic model problem with heterogeneous coefficients, as well as on an advection-diffusion problem with dominant microscopic transport.
date: 2015
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/18889/1/dissertation-maier-2015.pdf
identifier: DOI:10.11588/heidok.00018889
identifier: urn:nbn:de:bsz:16-heidok-188898
identifier:   Maier, Matthias Sebastian  (2015) Duality-based adaptivity of model and discretization in multiscale finite-element methods.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/18889/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng