Error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems

摘要

In this paper, we investigate error estimates and superconvergence of a mixed finite element method for elliptic optimal control problems. The gradient for our method belongs to the square integrable space instead of the classical H(div; Omega) space. The state and co state are approximated by the P-0(2)-P-1 (velocity-pressure) pair arid the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates in H-1-norm for the state and the co-state scalar functions, a priori error estimates in (L-2)(2) norm for the state and the co-state vector functions and a priori error estimates in L-2-norm for the control function. Then, using postprocessing projection operator, We derive a superconvergence result for the control variable. Next, we get a priori error estimates in L-2-norm for the state and the co-state scalar functions. Finally, a numerical example is given to demonstrate the theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.