A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems

In this paper, we discuss a priori error estimates and superconvergence of splitting positive definite mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element functions, and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates both for the control variable, the state variables and the co-state variables. Second, we obtain a superconvergence result for the control variable.