Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 4 : pp. 545–568
Abstract
In this article, we discuss and analyze discontinuous finite volume approximations of the distributed optimal control problems governed by a class of semilinear parabolic partial differential equations with control constraints. For the spatial discretization of the state and costate variables, piecewise linear elements are used and an implicit finite difference scheme is used for time derivatives; whereas, for the approximation of the control variable, three different strategies are used: variational discretization, piecewise constant and piecewise linear discretization. A priori error estimates (for these three approaches) in suitable $L^2$-norm are derived for state, co-state and control variables. Numerical experiments are presented in order to assure the accuracy and rate of the convergence of the proposed scheme.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-452
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 4 : pp. 545–568
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Semilinear parabolic optimal control problems variational discretization piecewise constant and piecewise linear discretization discontinuous finite volume methods a priori error estimates numerical experiments.