Adaptive space-time finite element methods for parabolic optimization problems

Dominik Meidner, Boris Vexler

Research output: Contribution to journalArticlepeer-review

116 Scopus citations

Abstract

In this paper we derive a posteriori error estimates 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 algorithm which successively improves the accuracy of the computed solution by construction of locally refined meshes for time and space discretizations.

Original languageEnglish
Pages (from-to)116-142
Number of pages27
JournalSIAM Journal on Control and Optimization
Volume46
Issue number1
DOIs
StatePublished - 2007
Externally publishedYes

Keywords

  • A posteriori error estimation
  • Mesh refinement
  • Optimal control
  • Parabolic equations
  • Parameter identification

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