Adaptive finite element methods for optimal control of second order hyperbolic equations

Abstract

In this paper we consider a posteriori error estimates for space-time finite element discretizations for optimal control of hyperbolic partial differential equations of second order. It is an extension of Meidner & 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 influences 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. © 2011 Institute of Mathematics.