Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

Publisher: Cambridge University Press

E-ISSN: 2075-1354|4|6|751-768

ISSN: 2070-0733

Source: Advances in Applied Mathematics and Mechanics, Vol.4, Iss.6, 2012-12, pp. : 751-768

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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 -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.