L^∞-error estimates of higher order mixed finite element approximations for elliptic optimal control problems

Abstract

In this paper, we investigate the L ^∞-error estimates of the numerical solutions of linear-quadratic elliptic control problems by using higher order mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k≥1). Optimal L ^∞-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for optimal control problems.

1991 AMS Subject Classifications:

• 49J20
• 65N30

Keywords:

• elliptic equations
• optimal control problems
• L ^∞-error estimates
• higher order mixed finite element methods
• Green's function