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Author: Borix Vexler
Title of the contribution: Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
Abstract:
In this talk we present an adaptive algorithm for efficient solution of optimization problems governed by parabolic partial differential equations. The discretization of the state equation is based on the space-time finite element method. We derive a posteriori error estimates which assess the error between the solution of the continuous and the discrete optimization problem with respect to a given quantity of interest. In order to set up an efficient adaptive algorithm we separate the influence of the time discretization, the space discretization and the discretization of the control variable. This allows to balance these types
of error and successively to improve the accuracy by construction of locally refined meshes for time, space and the control discretizations. We discuss numerical examples illustrating the behaviour of our method.
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