Weak Galerkin finite element methods for optimal control problems governed by second order elliptic equations

Abstract

This paper is concerned with the development of weak Galerkin (WG) finite element methods for optimal control problems governed by second order elliptic partial differential equations. WG methods are advantageous over other existing methods in that the control variable along the domain boundary is a natural variable by design in the numerical scheme. A convergence theory was established for the numerical solutions in various Sobolev norms. Numerical results are presented to demonstrate the efficiency and accuracy of the new scheme.