Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media. (15th August 2018)

• Record Type: Journal Article
• Authors: Kumar, Sarvesh; Ruiz-Baier, Ricardo; Sandilya, Ruchi
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 4(2018)
• Page Start: 923
• Page End: 937
• Publication Date: 2018-08-15
• Subjects: Optimal control problems -- Immiscible displacement in porous media -- Mixed formulations -- Finite volume element methods -- Error estimation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.05.031
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this article we introduce a family of discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid mixed/discontinuous approximation) measured in suitable norms are derived, showing optimal orders of convergence.