@inbook{3c2af621a90e44d8b0d9320898e2ee20,
title = "Petrov-galerkin crank-nicolson scheme for parabolic optimal control problems on nonsmooth domains",
abstract = "In this paper we transfer the a priori error analysis for the discretization of parabolic optimal control problems on domains allowing for H2 regularity (i.e. either with smooth boundary or polygonal and convex) to a large class of nonsmooth domains. We show that a combination of two ingredients for the optimal convergence rates with respect to the spatial and the temporal discretization is required. First we need a time discretization scheme which has the desired convergence rate in the smooth case. Secondly we need a method to treat the singularities due to non-smoothness of the domain for the corresponding elliptic state equation. In particular we demonstrate this philosophy with a Crank-Nicolson time discretization and finite elements on suitably graded meshes for the spatial discretization. A numerical example illustrates the predicted convergence rates.",
keywords = "Crank Nicolson scheme, Graded meshes, Non-smooth domains, Optimal control problem, Parabolic partial differential equation",
author = "Flaig, {Thomas G.} and Dominik Meidner and Boris Vexler",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.",
year = "2014",
doi = "10.1007/978-3-319-05083-6_26",
language = "English",
series = "International Series of Numerical Mathematics",
publisher = "Springer",
pages = "421--435",
booktitle = "International Series of Numerical Mathematics",
}