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Volume 11, Issue 4
Finite Element Approximation of Optimal Control for System Governed by Immiscible Displacement in Porous Media

Y. Chang, W. Cao, D. Yang, T. Sun & W. Liu

Int. J. Numer. Anal. Mod., 11 (2014), pp. 688-714.

Published online: 2014-11

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  • 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.

  • Keywords

Finite element approximation, optimal control problem, immiscible displacement.

  • AMS Subject Headings

65N30, 49J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-688, author = {Y. Chang, W. Cao, D. Yang, T. Sun and W. Liu}, title = {Finite Element Approximation of Optimal Control for System Governed by Immiscible Displacement in Porous Media}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/547.html} }
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 -

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.

Y. Chang, W. Cao, D. Yang, T. Sun and W. Liu. (2014). Finite Element Approximation of Optimal Control for System Governed by Immiscible Displacement in Porous Media. International Journal of Numerical Analysis and Modeling. 11 (4). 688-714. doi:
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