eprintid: 1871
rev_number: 12
eprint_status: archive
userid: 1
dir: disk0/00/00/18/71
datestamp: 2002-01-29 00:00:00
lastmod: 2014-04-03 11:29:39
status_changed: 2012-08-14 15:03:04
type: doctoralThesis
metadata_visibility: show
creators_name: Kapp, Hartmut Ulrich
title: Adaptive Finite Element Methods for Optimization in Partial Differential Equations
title_de: Adaptive Finite Elemente Methoden für Optimierung mit Partiellen Differentialgleichungen
ispublished: pub
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
keywords: A Posteriori Fehlerschätzer , adaptive Gitterverfeinerung , Ginzburg-Landau Modell , Navier-Stokes Gleichungen , Boussinesq Modelloptimal control problem , finite elements , a posteriori error estimates , mesh adaptation , Navier-Stokes equations
cterms_swd: Nichtlineare Optimierung
cterms_swd: Optimierung / Nebenbedingung
cterms_swd: Nichtlineare partielle Differentialgleichung
cterms_swd: Finite-Elemente-Methode
abstract_translated_text: A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates. These are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error. In this case, the computed state and co-state variables can be used as sensitivity factors multiplying the local cell-residuals in the error estimators. This results in a generic and efficient algorithm for mesh adaptation within the optimization process. Applications of the developed  method are boundary control problem models governed  by Ginzburg-Landau equations (superconductivity in semi-conductors),  by Navier-Stokes equations, and by the Boussinesq viscosity model (flow with temperature transport  for zero gravitation). Computations with more than 2 million unknowns were performed. 
abstract_translated_lang: eng
class_scheme: msc
class_labels: 65N30, 65K10, 49M37, 49J50, 49K20
date: 2000
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00001871
ppn_swb: 1643262238
own_urn: urn:nbn:de:bsz:16-opus-18711
date_accepted: 2001-12-13
advisor: HASH(0x561a6282a550)
language: eng
bibsort: KAPPHARTMUADAPTIVEFI2000
full_text_status: public
citation:   Kapp, Hartmut Ulrich  (2000) Adaptive Finite Element Methods for Optimization in Partial Differential Equations.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/1871/1/diss1.pdf
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/1871/2/diss2.pdf