Volume 4, Issue 6
Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

Yanping Chen ,  Tianliang Hou and Weishan Zheng

10.4208/aamm.12-12S05

Adv. Appl. Math. Mech., 4 (2012), pp. 751-768.

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  • Abstract

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L^2 and L^\infty-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.

  • History

Published online: 2012-12

  • AMS Subject Headings

49J20, 65N30

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