Adaptive space-time finite element methods for parabolic optimization problems

Dominik Meidner, Boris Vexler

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this paper we summerize recent results on a posteriori error estimation and adaptivity for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an efficient adaptive strategy producing economical (locally) refined meshes for each time step and an adapted time discretization. The space and time discretization errors are equilibrated, leading to an efficient method.

Original languageEnglish
Title of host publicationInternational Series of Numerical Mathematics
PublisherSpringer
Pages319-348
Number of pages30
DOIs
StatePublished - 2012

Publication series

NameInternational Series of Numerical Mathematics
Volume160
ISSN (Print)0373-3149
ISSN (Electronic)2296-6072

Keywords

  • A posteriori error estimation
  • Dynamic meshes
  • Mesh refinement
  • Optimal control
  • Parabolic equations
  • Parameter identification
  • Space-time finite elements

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