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Finite element simulations for compressible miscible displacement with molecular dispersion in porous media

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Abstract

We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium [5]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution and optimalH 1 error estimates are obtained. One contribution of this paper is a demonstration of how molecular dispersion can be handled.

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References

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

    MATH  Google Scholar 

  2. Douglas, J. Jr., Finite difference methods for two-phase incompressible flow in porous media,SIAM J. Numer. Anal.,20 (1983), 681–696.

    Article  MATH  Google Scholar 

  3. Douglas, J. Jr., Dupont, T. and Ewing R.E., Incomplete iteration for time-stepping a Galerkin method for a quasi-linear parabolic problem,SIAM J. Numer. Anal.,16 (1979), 503–522.

    Article  MATH  Google Scholar 

  4. Douglas, J. Jr., Ewing, R.E. and Wheeler, M.F., The approximation of the pressure by a mixed method in the simulation of miscible displacement,RIARO, Anal. Numér.,17 (1983), 17–33.

    MATH  Google Scholar 

  5. Douglas, J. Jr., Roberts, J.E., Numerical methods for a model for compressible miscible displacement in porous media,Math. Comp.,41 (1983), 441–459.

    Article  MATH  Google Scholar 

  6. Ewing, R.E. and Wheeler, M.F., Galerkin methods for miscible displacement problems in porous media,SIAM J. Numer. Anal.,17 (1980), 351–365.

    Article  MATH  Google Scholar 

  7. Jaffre, J. and Roberts, E., Upstream weighting and mixed finite elements in the simulation of miscible displacements,RIARO, Anal. Numer.,19 (1985), 443–460.

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Wheeler, M.F., A prioriL 2-error estimates for Galerkin approximations to parabolic partial differential equations,SIAM J. Numer. Anal.,10 (1973), 723–739.

    Article  MATH  Google Scholar 

  10. Wheeler, M.F. and Darlow, B.L., Interior penalty Galerkin procedures for miscible displacement problems in porous media, in: Computational Methods in Nonlinear Mecahnics (Oden, J.T., ed.), North-Holland, Amsterdam, 1980.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shandong Teacher’s University, 250014, Jinan

    Chen Huanzhen & Li Qian

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  1. Chen Huanzhen
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  2. Li Qian
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Additional information

The work is supported by Science Foundation of the Educational Committee of Shandong Province.

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Chen, H., Li, Q. Finite element simulations for compressible miscible displacement with molecular dispersion in porous media. Appl. Math. 11, 17–32 (1996). https://doi.org/10.1007/BF02662177

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  • DOI: https://doi.org/10.1007/BF02662177

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