Error estimates of characteristic finite elements for bilinear convection–diffusion optimal control problems

Abstract

This paper investigates a fully discrete characteristic finite element approximation of bilinear unsteady convection–diffusion optimal control problems. The characteristic line method is used to treat the convection term and the finite element method is adopted to treat the diffusion term. The state and adjoint state are discretized by piecewise linear functions, the control is approximated by piecewise constant functions. A priori error estimates are derived for the state, adjoint state and control variables. Some numerical examples are provided to confirm our theoretical findings.