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BY-NC-ND 4.0 license Open Access Published by De Gruyter January 1, 2011

Adaptive Finite Element Methods For Optimal Control Of Second Order Hyperbolic Equations

  • Axel Kröner EMAIL logo


In this paper we consider a posteriori error estimates for space-time finite element discretizations for optimal control of hyperbolic partial dierential equations of second order. It is an extension of Meidner and Vexler (2007), where optimal control problems of parabolic equations are analyzed. The state equation is formulated as a first order system in time and a posteriori error estimates are derived separating the in uences of time, space, and control discretization. Using this information the accuracy of the solution is improved by local mesh refinement. Numerical examples are presented. Finally, we analyze the conservation of energy of the homogeneous wave equation with respect to dynamically in time changing spatial meshes.

Received: 2010-11-06
Revised: 2011-03-16
Accepted: 2011-04-21
Published Online: 2011
Published in Print: 2011

© Institute of Mathematics, NAS of Belarus

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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