Convergence of MPFA on hexahedra

SPE Reservoir Simulation Symposium Proceedings

Volumn 2, Issue , 2009, Pages 1296-1313

  Matringe, S F ^a   Juanes, R ^b   Tchelepi, H A ^a  

^a STANFORD UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CENTERED FINITE DIFFERENCES; DEGREES OF FREEDOM; FOUR-DEGREES-OF-FREEDOM; MIXED FINITE ELEMENT METHODS; MIXED FINITE ELEMENTS; MULTIPOINT; NUMERICAL EXPERIMENTS; NUMERICAL QUADRATURE; NUMERICAL SOLUTION; OPTIMAL ERROR ESTIMATE; RECTANGULAR PARALLELEPIPEDS; SCALAR AND VECTOR FIELDS; SECOND ORDER ELLIPTIC; TENSOR COEFFICIENTS; UNSTRUCTURED GRID; VELOCITY FIELD;

ERROR ANALYSIS; FINITE DIFFERENCE METHOD; MECHANICS; PETROLEUM RESERVOIR EVALUATION; SOLAR RADIATION;

TENSORS;

EID: 70449597827     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. I. Aavatsmark. An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci., 6:405-432, 2002.
2. T. Arbogast, M. F. Wheeler, and I. Yotov. Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal, 34:828-852, 1997.
3. I. Babuska. The finite element method with Lagrangian multipliers. Numer. Math., 20:179-192, 1973.
4. S. C. Brenner and L. R. Scott. The Mathematical Theory of Finite Element Methods, volume 15 of Texts in Applied Mathematics. Springer-Verlag, New York, 1994.
5. F. Brezzi. On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO Anal. Numer., 8:129-151, 1974.
6. F. Brezzi, J. Douglas, Jr., R. Duran, and M. Fortin. Mixed finite elements for second order elliptic problems in three variables. Numer. Math., 51:237-250, 1987.
7. F. Brezzi, J. Douglas, Jr., and L. D. Marini. Two families of mixed finite elements for second order elliptic problems. Numer. Math., 47:217-235, 1985.
8. F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods, volume 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York, 1991.
9. Z. Cai, J. Douglas, Jr., and M. Park. Development and analysis of higher order finite volume methods over rectangles for elliptic equations. Adv. Comput. Math., 19:3-33, 2003.
10. Z. X. Chen and X. J. Yu. Implementation of mixed methods as finite difference methods and applications to nonisother-mal multiphase flow in porous media. J. Comput. Math., 24(3):281-294, 2006.
11. P. G. Ciarlet. The finite element method for elliptic problems. North-Holland, Amsterdam, 1978.
12. T. Dupont and R. Scott. Polynomial approximation of functions in Sobolev spaces. Math. Comp., 34(150):441-463, 1980.
13. M. G. Edwards and C. F. Rogers. Finite-volume discretization with imposed flux continuity for the general tensor pressure equation. Comput. Geosci., 2:259-290, 1998.
14. R. A. Klausen and R. Winther. Convergence of multipoint flux approximations on quadrilateral grids. Numer. Methods Partial Differential Equations, 22(6):1438-1454, 2006.
15. R. A. Klausen and R. Winther. Robust convergence of multi point flux approximations on rough grids. Numer. Math., 104(3):317-337, 2006.
16. S. H. Lee, P. Jenny, and H. A. Tchelepi. A finite-volume method with hexahedral multiblock grids for modeling flow in porous media. Comput. Geosci., 6:353-379, 2002.
17. J. E. Marsden and T. J. R. Hughes. Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs, NJ, 1983. Reprinted with corrections, Dover, New York, 1994.
18. S. F. Matringe, R. Juanes, and H. A. Tchelepi. Robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids. J. Comput. Phys., 219:992-1012, doi:10.1016/j.jcp. 2006.07.004, 2006.
19. S. F. Matringe, R. Juanes, and H. A. Tchelepi. Mixed finite element and related control volume discretizations for reservoir simulation on three-dimensional unstructured grids. In SPE Reservoir Simulation Symposium, Houston, TX, February 26-28 2007. (SPE 106117).
20. S. F. Matringe, R. Juanes, and H. A. Tchelepi. Streamline tracing on general triangular or quadrilateral grids. Soc. Pet. Eng. J., 12(2): pp. 217-233, June 2007.
21. 3. Numer. Math., 35:315-341, 1980.
22. P. A. Raviart and J. M. Thomas. A mixed finite element method for second order elliptic problems. In I. Galligani and E. Magenes, editors, Mathematical Aspects of the Finite Element Method, volume 606 of Lecture Notes in Mathematics, pages 292-315, New York, 1977. Springer-Verlag.
23. T. F. Russell and M. F. Wheeler. Finite element and finite difference methods for continuous flows in porous media. In R. E. Ewing, editor, The Mathematics of Reservoir Simulation, pages 35-106. SIAM, Philadelphia, PA, 1983.
24. A. Weiser and M. F. Wheeler. On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal, 25(2):351-375, 1988.
25. M. F. Wheeler and I. Yotov. A multipoint flux mixed finite element method. SIAM J. Numer. Anal, 44(5):2082-2106, 2006.