Finite element methods for an optimal steady‐state control problem

Abstract

SUMiMARYAn optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is stated that, for minimum computational effort and high accuracy, 'mixed' finite elements requiring only Co continuity, and approximating the control and state functions simultaneously are better suited to similar 'fourth order' problems.