Finite Element Approximation of Elliptic Dirichlet Optimal Control Problems

Abstract

We develop a priori error analysis for the finite element Galerkin discretization of elliptic Dirichlet optimal control problems. The state equation is given by an elliptic partial differential equation and the finite dimensional control variable enters the Dirichlet boundary conditions. We prove the optimal order of convergence and present a numerical example confirming our results.

Keywords:

• Dirichlet boundary control
• Error estimates
• Finite elements
• Optimal control

AMS Subject Classification:

• 65N30
• 65N15
• 35J05
• 49K20