An Improved Finite Element Approximation and Superconvergence for Temperature Control Problems

Abstract

In this paper, we consider an improved finite element approximation for temperature control problems, where the state and the adjoint state are discretized by piecewise linear functions while the control is not discretized directly. The numerical solution of the control is obtained by a projection of the adjoint state to the set of admissible controls. We derive a priori error estimates and superconvergence of second-order. Moreover, we present some numerical examples to illustrate our theoretical results.

Keywords:

• optimal control
• finite element method
• approximation
• convergence analysis

AMS Subject Classification:

• 49J20
• 65M60
• 80M10