Mixed finite element methods for generalized forchheimer flow in porous media

被引：80
作者：
Park, EJ [1 ]
机构：
[1] Yonsei Univ, Dept Math, Seoul 120749, South Korea
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 21卷 / 02期
关键词：
non-Darcy flow; Forchheimer's law; mixed methods; error estimates;
D O I：
10.1002/num.20035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in R-d, d less than or equal to 3, subject to Forchhheimer's law-a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L-infinity(J; L-2(Omega)) and in Linfinity(J; H(div; Omega)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L-infinity(J; L-infinity(Omega)) for the pressure. (C) 2004 Wiley Periodicals. Inc.
引用
收藏
页码：213 / 228
页数：16
相关论文
共 32 条
[21]   Mixed finite element domain decomposition for nonlinear parabolic problems [J].
Kim, MY ;
Park, EJ ;
Park, J .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 40 (8-9) :1061-1070
[22]   Fully discrete mixed finite element approximations for non-Darcy flows in porous media [J].
Kim, MY ;
Park, EJ .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 38 (11-12) :113-129
[23]   A MIXED FINITE-ELEMENT METHOD FOR A STRONGLY NONLINEAR 2ND-ORDER ELLIPTIC PROBLEM [J].
MILNER, FA ;
PARK, EJ .
MATHEMATICS OF COMPUTATION, 1995, 64 (211) :973-988
[24]  
MILNER FA, 1985, MATH COMPUT, V44, P303, DOI 10.1090/S0025-5718-1985-0777266-1
[25]   MIXED FINITE-ELEMENTS IN IR3 [J].
NEDELEC, JC .
NUMERISCHE MATHEMATIK, 1980, 35 (03) :315-341
[26]  
Park E.J., 1996, NUMER METH PART D E, V12, P41, DOI DOI 10.1002/(SICI)1098-2426(199601)12:1<41::AID-NUM2>3.0.CO
[27]  
2-N
[28]   MIXED FINITE-ELEMENT METHODS FOR NONLINEAR 2ND-ORDER ELLIPTIC PROBLEMS [J].
PARK, EJ .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (03) :865-885
[29]  
Raviart P.A., 1977, LECT NOTES MATH, V606, P292, DOI DOI 10.1007/BFB0064470
[30]   ON THE DERIVATION OF THE FORCHHEIMER EQUATION BY MEANS OF THE AVERAGING THEOREM [J].
RUTH, D ;
MA, HP .
TRANSPORT IN POROUS MEDIA, 1992, 7 (03) :255-264
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