TY - JOUR
T1 - Finite Element  Approximation of Optimal Control for System Governed by Immiscible Displacement in Porous Media
AU - Y. Chang, W. Cao, D. Yang, T. Sun & W. Liu
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 688
EP - 714
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/547.html
KW - Finite element approximation, optimal control problem, immiscible displacement.
AB - <p style="text-align: justify;">In this work, we study the finite element approximation of a model optimal control problem governed by the system describing the two-phase incompressible flow in porous media,
with the aim to maximize production of oil from petroleum reservoirs. We first give the proof for
the existence of the solutions of the control problem. The optimality conditions are then obtained
and the existence of the solution of the adjoint equations is shown. After that we consider its
finite element approximation. We have obtained the a priori error estimates with the optimal
orders and minimum regularity requirements. Finally, we carry out some numerical tests.</p>