L ∞-error estimates of triangular mixed finite element methods for optimal control problems governed by semilinear elliptic equations

Abstract

We look at L ∞-error estimates for convex quadratic optimal control problems governed by nonlinear elliptic partial differential equations. In so doing, use is made of mixed finite element methods. The state and costate are approximated by the lowest order Raviart-Thomas mixed finite element spaces, and the control, by piecewise constant functions. L ∞-error estimates of optimal order are derived for a mixed finite element approximation of a semilinear elliptic optimal control problem. Finally, numerical tests are presented which confirm our theoretical results.