Analysis and comparison of mixed finite element and multipoint flux approximation methods for homogeneous media |
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Authors: | Trond Mannseth |
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Institution: | (1) Centre for Integrated Petroleum Research, University of Bergen, Bergen, Norway;(2) Department of Mathematics, University of Bergen, Bergen, Norway |
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Abstract: | We consider discretization on quadrilateral grids of an elliptic operator occurring, for example, in the pressure equation
for porous-media flow. In a realistic setting – with non-orthogonal grid, and anisotropic, heterogeneous permeability – special
discretization techniques are required. Mixed finite element (MFE) and multipoint flux approximation (MPFA) are two methods
that can handle such situations. Previously, a framework for analytical comparison of MFE and MPFA in special cases has been
suggested. A comparison of MFE and MPFA-O (one of two main variants of MPFA) for isotropic, homogeneous permeability on a
uniformly distorted grid was also performed. In the current paper, we utilize the suggested framework in a slightly different
manner to analyze and compare MFE, MPFA-O and MPFA-U (the second main variant of MPFA). We reconsider the case previously
analyzed. We also consider the case of generally anisotropic, homogeneous permeability on an orthogonal grid. |
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Keywords: | analysis general anisotropy mixed finite element multipoint flux approximation uniformly distorted grid |
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