A priori error estimates for finite element discretizations of a shape optimization problem
Revised: 5 March 2013
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.
Mathematics Subject Classification: 49Q10 / 49M25 / 65M15 / 65M60
Key words: Shape optimization / existence and convergence of approximate solutions / error estimates / finite elements
© EDP Sciences, SMAI 2013