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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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)
Ciarlet, P.G. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978
Dawson, C.N., Dopont, T.F. Explicit/ implicit conservative Galerkin domain decomposition procedures for parabolic problems. Math. Comp., 58(197): 21–34 (1992)
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)
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)
Douglas, Jr J. Finite difference method for two-phase incompressible flow in porous media. SIAM J. Numer. Anal., 20(4): 681–691 (1983)
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
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)
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)
Ewing, R.E. The Mathematics of Reservoir Simulation. Philadelphia: SIAM, 1983
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
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)
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)
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)
Ungerer, P. Fluid flow, hydrocarbon gereration and migration. AAPG Bull., 74(3): 309–335 (1990)
Ungerer, P., Dolyiez, B., Chenet, P.Y., et al. Migration of hydrocarbon in sedimentary basins. Doliges B, ed. Editions Technip, Paris, 414–455, 1987
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)
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)
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)
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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
Keywords
- Coupled system of dynamics of fluids
- domain decomposition
- characteristic finite element
- parallel arithmetic
- L2 error estamate