Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

被引：6

作者：

Kumar, Sarvesh ^{[1
]}

Ruiz-Baier, Ricardo ^{[2
]}

Sandilya, Ruchi ^{[3
]}

机构：

[1] Indian Inst Space Sci & Technol, Dept Math, Thiruvananthapuram 695547, Kerala, India

[2] Univ Oxford, Math Inst, A Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[3] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Optimal control problems; Immiscible displacement in porous media; Mixed formulations; Finite volume element methods; Error estimation; MISCIBLE DISPLACEMENT PROBLEMS; GALERKIN METHODS; UNIFIED ANALYSIS; MULTIPHASE FLOW; REACTIVE TRANSPORT; COUPLED FLOW; 2-PHASE FLOW; APPROXIMATION; DISCRETIZATION; OPTIMIZATION;

D O I：

10.1016/j.camwa.2018.05.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：923 / 937

页数：15

共 49 条

[1]

[Anonymous], 2006, Comput. Sci. Eng.

[2]

[Anonymous], MIXED AND HYBRID FIN

[3] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[4] DISCONTINUOUS GALERKIN FINITE ELEMENT CONVERGENCE FOR INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS OF LOW REGULARITY [J].

Bartels, Soeren ;

Jensen, Max ;

Mueller, Ruediger .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (05) :3720-3743

[5] A discontinuous finite volume element method for second-order elliptic problems [J].

Bi, Chunjia ;

Liu, Mingming .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (02) :425-440

[6] Discontinuous Finite Volume Element Method for Parabolic Problems [J].

Bi, Chunjia ;

Geng, Jiaqiang .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (02) :367-383

[7] Dynamic optimization of waterflooding with smart wells using optimal control theory [J].

Brouwer, DR ;

Jansen, JD ;

Inil, S .

SPE JOURNAL, 2004, 9 (04) :391-402

[8] Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation [J].

Buerger, Raimund ;

Kumar, Sarvesh ;

Ruiz-Baier, Ricardo .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 299 :446-471

[9] A STABILIZED FINITE VOLUME ELEMENT FORMULATION FOR SEDIMENTATION-CONSOLIDATION PROCESSES [J].

Buerger, Raimund ;

Ruiz-Baier, Ricardo ;

Torres, Hector .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (03) :B265-B289

[10] COUPLING OF DISCONTINUOUS GALERKIN SCHEMES FOR VISCOUS FLOW IN POROUS MEDIA WITH ADSORPTION [J].

Burger, Raimund ;

Kenettinkara, Sudarshan Kumar ;

Baier, Ricardo Ruiz ;

Torres, Hector .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (02) :B637-B662

← 1 2 3 4 5 →