TY - JOUR
T1 - On Discontinuous Finite Volume Approximations for Semilinear Parabolic Optimal Control Problems
AU - R. Sandilya & S. Kumar
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 545
EP - 568
PY - 2016
DA - 2016/07
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/452.html
KW - Semilinear parabolic optimal control problems, variational discretization, piecewise constant and piecewise linear discretization, discontinuous finite volume methods, a priori error estimates, numerical experiments.
AB - <p style="text-align: justify;">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.</p>