Interpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problems

Abstract

ABSTRACTIn this paper, we study a priori error estimates of interpolation coefficients mixed finite element methods for semilinear Dirichlet boundary optimal control problems. Using the interpolation coefficient thought to process the nonlinear term of equations, we present the mixed finite element approximation with interpolated coefficients for general optimal control problems governed by semilinear Dirichlet boundary elliptic equations. The state variable and the co-state variable are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is discretized by piecewise constant elements. We derive a priori error estimates in norm and norm for the coupled state and control variables with optimal convergence order. Finally, some numerical examples are given to confirm our theoretical results.