Finite Element Approximation of Optimal Control for System Governed by Immiscible Displacement in Porous Media
Year: 2014
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 688–714
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-547
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 4 : pp. 688–714
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Finite element approximation optimal control problem immiscible displacement.