Interpolated coefficient characteristic finite element method for semilinear convection–diffusion optimal control problems

Abstract

In this paper, a fully discrete interpolated coefficient characteristic finite element approximation is proposed for optimal control problems governed by time-dependent semilinear convection–diffusion equations, where the hyperbolic part of the state equation is first treated by directional derivatives and then discretized by backward difference, the semilinear term is dealt with interpolation coefficient finite elements technique. A priori error estimates for the control, state and co-state variables are derived. Theoretic results are confirmed by a numerical example.

Keywords

• Interpolated coefficient characteristic finite element method
• Semilinear convection–diffusion equations
• Optimal control problems
• A priori error estimates