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A mixed and discontinuous Galerkin finite volume element method for incompressible miscible displacement problems in porous media

Authors

  • Sarvesh Kumar

    Corresponding author
    1. Department of Mathematics, Birla Institute of Technology and Science, Pilani-K.K. Goa Campus, Zuarinagar-403726, Goa, India
    • Department of Mathematics, Birla Institute of Technology and Science, Pilani-K.K. Goa Campus, Zuarinagar-403726, Goa, India
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Abstract

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this article, we present a mixed finite volume element method for the approximation of pressure-velocity equation and a discontinuous Galerkin finite volume element method for the concentration equation. A priori error estimates in L(L2) are derived for velocity, pressure, and concentration. Numerical results are presented to substantiate the validity of the theoretical results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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