A priori and a posteriori error estimates for the method of lumped masses for parabolic optimal control problems

Abstract

In this paper, we examine the method of lumped masses for the approximation of convex optimal control problems governed by linear parabolic equations, where the lumped mass method is used for the discretization of the state equation. We derive some a priori and a posteriori error estimates for both the state and control approximations with control constraints of obstacle type. Numerical experiments are given to show the efficiency and reliability of the lumped mass method.

Keywords:

• optimal control
• the method of lumped masses
• a priori error estimates
• a posteriori error estimates

2000 AMS Subject Classifications :

• 49J20
• 65M60

Acknowledgements

This research was supported by the National Basic Research Program of China (No. 2007CB814906) and the National Natural Science Foundation of China (No. 10771124).