Volume 2, Issue 1
Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

Adv. Appl. Math. Mech., 2 (2010), pp. 56-75.

Published online: 2010-02

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• Abstract

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables  and use piecewise constant functions to approximate the control variable. We obtain the superconvergence of $\mathcal{O}(h^{1+s})$ $(0$<$s\leq$<$1)$ for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.

• Keywords

Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties

• AMS Subject Headings

49J20 65N30

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables  and use piecewise constant functions to approximate the control variable. We obtain the superconvergence of $\mathcal{O}(h^{1+s})$ $(0$<$s\leq$<$1)$ for the control variable. Finally, we present two numerical examples to confirm our superconvergence results.