A priori error estimates for finite element discretizations of a shape optimization problem

Bernhard Kiniger, Boris Vexler

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples.

Original languageEnglish
Pages (from-to)1733-1763
Number of pages31
JournalMathematical Modelling and Numerical Analysis
Volume47
Issue number6
DOIs
StatePublished - 2013

Keywords

  • Error estimates
  • Existence and convergence of approximate solutions
  • Finite elements
  • Shape optimization

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