Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

Year:    2013

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 3 : pp. 209–227

Abstract

In this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the $L^2$ projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.030713.100813a

East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 3 : pp. 209–227

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Superconvergence finite element methods optimal control problems parabolic equations interpolation operator.

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