Adaptive finite element methods for optimal control ofelastic waves

Abstract

Abstract In this paper a posteriori error estimates for space-time finite element discretizations for optimal control problems governed by the dynamical Lame system are considered using the dual weighted residual method (DWR). We apply techniques developed in Kroner (2011a), where optimal control problems for second order hyperbolic equations are considered. The provided error estimator separates the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an adaptive algorithm which improves the accuracy of the computed solutions by construction of locally refined meshes. We present a numerical example showing a speedup in cpu-time as well as a reduction in degrees of freedom in comparison to uniform mesh refinement.