Implementation of Mixed Methods as Finite Difference Methods and Applications to Nonisothermal Multiphase Flow in Porous Media
Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 281–294
Abstract
In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglas-Marini elements (if $d=2$) or Brezzi-Douglas-Durán-Fortin elements (if $d=3$) on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as a simple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient, the sparsity pattern for the scalar unknown is a five point stencil if $d=2$, and seven if $d=3$. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively. Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8752
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 281–294
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Finite difference Implementation Mixed method Error estimates Superconvergence Tensor coefficient Nonisothermal multiphase Multicomponent flow Porous media.