Volume 3, Issue 3
Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

Yuelong Tang and Yanping Chen

10.4208/eajam.030713.100813a

East. Asia. J. Appl. Math., 3 (2013), pp. 209-227.

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  • 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.

  • History

Published online: 2018-02

  • AMS Subject Headings

35B37, 49J20, 65N30

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