TY - JOUR
T1 - Convergence of Discontinuous Finite Volume Discretizations for a Semilinear Hyperbolic Optimal Control Problem
AU - R. Sandilya & S. Kumar
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 926
EP - 950
PY - 2016
DA - 2016/11
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/472.html
KW - 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.
AB - <p style="text-align: justify;">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.</p>