Functional a posteriori error estimates for optimal control problems with elliptic constraints

Dr. Olli Mali

Oct. 28, 2014, 3:30 p.m. S2 059

Two-sided error estimates are presented for a class of optimal control problems generated by a quadratic cost functional, a linear elliptic state equation, and a convex constraint for the control. It is assumed that the state discrepancy in the cost functional is evaluated using the norm generated by the bilinear form of the respective elliptic state equation. Then, the standard functional a posteriori error estimates developed by S. Repin in mid 90's for the state equation can be used to generate estimates for the cost function value. These estimates are guaranteed and do not require a solution of a PDE. For a certain error quantity, estimates for the cost functional can be used to derive again two-sided estimates. The close relation between all estimates and the necessary conditions of the optimal control problem are emphasized. Moreover, different numerical error estimation methods generated by these estimates are discussed and some numerical tests are presented.