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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