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

Yanping Chen ,  Li Dai and Zuliang Lu

10.4208/aamm.09-m0931

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

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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.

  • History

Published online: 2010-02

  • AMS Subject Headings

49J20, 65N30

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