A Priori Error Analysis of the Petrov-Galerkin Crank-Nicolson Scheme for Parabolic Optimal Control Problems

Authors:
Dominik Meidner;Boris Vexler
Affiliations:
meidner@ma.tum.de and vexler@ ma.tum.de;-
Venue:
SIAM Journal on Control and Optimization
Year:
2011

Citing 12
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Abstract

In this paper, a finite element discretization of an optimal control problem governed by the heat equation is considered. The temporal discretization is based on a Petrov-Galerkin variant of the Crank-Nicolson scheme, whereas the spatial discretization employs usual conforming finite elements. With a suitable postprocessing step, a discrete solution is obtained for which error estimates of optimal order are proven. A numerical result is presented for illustrating the theoretical findings.