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Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

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Abstract

For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L2 norm are derived for the error in the approximate solution.

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References

  1. Bredehoeft, J.D., Pinder, G.F. Digital analysis of areal flow in multiaquifer groundwater systems: A quasidimensional model. Water Resources Research, 6(3): 883–888 (1970)

    Article  Google Scholar 

  2. Ciarlet, P.G. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978

  3. Dawson, C.N., Dopont, T.F. Explicit/ implicit conservative Galerkin domain decomposition procedures for parabolic problems. Math. Comp., 58(197): 21–34 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dawson, C.N., Du, Q., Dupont, T.F. A finite difference domain decomposition algorithm for numerical solution of the heat equation. Math. Comp., 57(195): 63–71 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Don, W., Emil, O.F. An iterative quasi-three-dimensional finite element model for heterogeneous multiaquifer systems. Water Resources Research, 14(5): 943–952 (1976)

    Google Scholar 

  6. Douglas, Jr J. Finite difference method for two-phase incompressible flow in porous media. SIAM J. Numer. Anal., 20(4): 681–691 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  7. Douglas, Jr J. Form nonconservative to locally conservative Eulerian-Lagran numerical methods and their application to nonlinear transport. An International Workshop of Computational Physics: Fluid Flow and Transport in Porous Media, August 2–6, 1999, Beijing

  8. Douglas, Jr J., Russell, T.F. Numerical method for convection-dimenated diffusion problems based on combining the method of characteristics with finite element or finite diference procedures. SIAM J. Numer. Anal., 19(5): 871–885 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  9. Douglas, Jr J., Yuan, Yirang. Numerical simulation of immiscible flow in porous media based on combining the method of characteristics with finite element procedures. Numerical Simulation in Oil Recovery, Wheeler M.F. Editor, Spring-Verlag, 119–131 (1988)

  10. Ewing, R.E. The Mathematics of Reservoir Simulation. Philadelphia: SIAM, 1983

  11. Ewing, R.E. Mathematical modeling and simulation of multiphase flow in porous media. An In International Workshop of Computational physics: Fluid Flow and Transport in Porous Media, August 2–6, 1999, Beijing

  12. Ewing, R.E., Russell, T.F., Wheeler, M.F. Convergence analysis of on approximation of miscible displacement in porous media of mixed finite elements and a modified method of characteristics. Computer Meth. Appl. Mech. Eng., 47: 73–92 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ewing, R.E., Yuan, Y.R., Li, G. A tine-diseretization procedure for a mixed finite element approximation for compressible flow of contamination from nuclear waste in porous media. SIAM J. Numer. Anal., 26(6): 1513–1524 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  14. Russell, T.F. Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media. SIAM J. Numer. Anal., 22(5): 970–1013 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ungerer, P. Fluid flow, hydrocarbon gereration and migration. AAPG Bull., 74(3): 309–335 (1990)

    Google Scholar 

  16. Ungerer, P., Dolyiez, B., Chenet, P.Y., et al. Migration of hydrocarbon in sedimentary basins. Doliges B, ed. Editions Technip, Paris, 414–455, 1987

  17. Wheeler, M.F. A prior L2 error estimates for Galerkin approximation to parabolic partial differential equation. SIAM J. Numer. Anal., 10(4): 723–759 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yuan, Yirang. The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application. Science in China (Series A), 45(5): 578–593 (2002)

    MATH  Google Scholar 

  19. Yuan, Yirang. The characteristic finite difference fractional steps methods for compressible two-phase displacement problem. Science in China (Series A), 42(1): 48–57 (1999)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, China

    Yi-rang Yuan

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  1. Yi-rang Yuan
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Correspondence to Yi-rang Yuan.

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Supported by the Major State Basic Research Program of China (No. 1999032803), the National Tackling Key Problems Program (No. 2002020094), the National Natural Sciences Foundation of China (Nos.19972039, 10271066) and the Doctorate Foundation of the Ministry of Education of China (No.2003042047).

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Yuan, Yr. Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media. Acta Mathematicae Applicatae Sinica, English Series 23, 255–268 (2007). https://doi.org/10.1007/s10255-007-0368-1

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  • DOI: https://doi.org/10.1007/s10255-007-0368-1

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