ON DISCONTINUOUS FINITE VOLUME APPROXIMATIONS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS

In this article, we discuss and analyze discontinuous finite volume approximations of the distributed optimal control problems governed by a class of semilinear parabolic partial differential equations with control constraints. For the spatial discretization of the state and costate variables, piecewise linear elements are used and an implicit finite difference scheme is used for time derivatives; whereas, for the approximation of the control variable, three different strategies are used: variational discretization, piecewise constant and piecewise linear discretization. A priori error estimates (for these three approaches) in suitable L-2-norm are derived for state, co-state and control variables. Numerical experiments are presented in order to assure the accuracy and rate of the convergence of the proposed scheme.