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Numerical Study of Mixed Finite Element and Multi Point Flux Approximation of Flow in Porous Media

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. Bause

    (University of Erlangen-Nuremberg, Department Mathematics)

  • J. Hoffmann

    (University of Erlangen-Nuremberg, Department Mathematics)

Abstract

In this paper the numerical performance properties of some locally mass conservative numerical schemes for simulating flow in a porous medium are studied. In particular, the accuracy of approximations of flows with discontinuous permeability tensors and on irregular grids is analysed. We consider the mixed finite element approach with the lowest order Raviart-Thomas (RT0) and Brezzi-Douglas-Marini (BDM1) element and a multi point flux approximation (MPFA) control volume method. The BDM1 method yields a second order accurate approximation of the flux whereas the RT0 and MPFA approach are of first order accuracy only. MPFA methods offer explicit discrete fluxes which is not possible to get from mixed finite element methods and allows a wider class of applications.

Suggested Citation

  • M. Bause & J. Hoffmann, 2008. "Numerical Study of Mixed Finite Element and Multi Point Flux Approximation of Flow in Porous Media," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 433-440, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_51
    DOI: 10.1007/978-3-540-69777-0_51
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