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

2011; Society for Industrial and Applied Mathematics; Volume: 49; Issue: 5 Linguagem: Inglês

10.1137/100809611

1095-7138

Dominik Meidner, Boris Vexler,

Advanced Mathematical Modeling in Engineering

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.