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 language | English |
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Pages (from-to) | 1733-1763 |
Number of pages | 31 |
Journal | Mathematical Modelling and Numerical Analysis |
Volume | 47 |
Issue number | 6 |
DOIs | |
State | Published - 2013 |
Keywords
- Error estimates
- Existence and convergence of approximate solutions
- Finite elements
- Shape optimization