An adaptive numerical method for semi-infinite elliptic control problems based on error estimates

Abstract

We discuss numerical reduction methods for an optimal control problem of semi-infinite type with finitely many control parameters but infinitely many constraints. We invoke known a priori error estimates to reduce the number of constraints. In a first strategy, we apply uniformly refined meshes, whereas in a second more heuristic strategy we use adaptive mesh refinement and provide an a posteriori error estimate for the control based on perturbation arguments.

Keywords:

• optimal control
• elliptic partial differential equation
• FEM
• semi-infinite programming
• numerical methods

AMS Subject Classification:

• 49J20
• 80M10
• 49N05
• 90C34
• 41A25
• 90C34