TY - JOUR
T1 - Variational Discretization for Optimal Control Governed by Convection Dominated Diffusion Equations
AU - Michael Hinze, Ningning Yan & Zhaojie Zhou
JO - Journal of Computational Mathematics
VL - 2-3
SP - 237
EP - 253
PY - 2009
DA - 2009/04
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8570.html
KW - Constrained optimal control problem, Convection dominated diffusion equation, Edge stabilization Galerkin method, Variational discretization, A priori error estimate, A posteriori error estimate.
AB - <p style="text-align: justify;">In this paper, we study variational discretization for the constrained optimal control
problem governed by convection dominated diffusion equations, where the state equation
is approximated by the edge stabilization Galerkin method. A priori error estimates are
derived for the state, the adjoint state and the control. Moreover, residual type a posteriori
error estimates in the $L^2$-norm are obtained. Finally, two numerical experiments are
presented to illustrate the theoretical results.</p>