eprintid: 18889
rev_number: 17
eprint_status: archive
userid: 1886
dir: disk0/00/01/88/89
datestamp: 2015-07-01 11:17:33
lastmod: 2015-07-09 08:09:27
status_changed: 2015-07-01 11:17:33
type: doctoralThesis
metadata_visibility: show
creators_name: Maier, Matthias Sebastian
title: Duality-based adaptivity of model and discretization in multiscale finite-element methods
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
cterms_swd: Numerical Mathematics
cterms_swd: Dual Weighted Residual Method
cterms_swd: Multiscale Methods
cterms_swd: Model Adaptivity
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00018889
ppn_swb: 1657365921
own_urn: urn:nbn:de:bsz:16-heidok-188898
date_accepted: 2015-06-12
advisor: HASH(0x55de57d063b0)
language: eng
bibsort: MAIERMATTHDUALITYBAS2015
full_text_status: public
citation:   Maier, Matthias Sebastian  (2015) Duality-based adaptivity of model and discretization in multiscale finite-element methods.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/18889/1/dissertation-maier-2015.pdf