Convergence of Discontinuous Finite Volume Discretizations for a Semilinear Hyperbolic Optimal Control Problem
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 926–950
Abstract
In this paper, we discuss discontinuous finite volume approximations of the distributed optimal control problems governed by a class of semilinear hyperbolic partial differential equations with control constraints. The spatial discretization of the state and costate variables follows discontinuous finite volume schemes with piecewise linear elements, whereas three different strategies are used for the control approximation: variational discretization, piecewise constant and piecewise linear discretization. As the resulting semi-discrete optimal system is non-symmetric, we have employed optimize then discretize approach to approximate the control problem. A priori error estimates for control, state and costate variables are derived in suitable natural norms. The present analysis is an extension of the analysis given in Kumar and Sandilya [Int. J. Numer. Anal. Model. (2016), 13: 545-568]. Numerical experiments are presented to illustrate the performance of the proposed scheme and to confirm the predicted accuracy of the theoretical convergence rates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-472
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 926–950
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Semilinear hyperbolic optimal control problems variational discretization piecewi- se constant and piecewise linear discretization discontinuous finite volume meth- ods a priori error estimates numerical experiments.