A priori error estimates of mixed finite element methods for general semilinear elliptic optimal control problems

摘要

We study a priori error estimates of mixed finite element methods for general convex optimal control problems governed by semilinear elliptic equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces, and the control is discretized by piecewise constant elements. We derive a priori error estimates for the coupled state and control approximation. Finally, we present some numerical examples which confirm our theoretical results.