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A mixed finite volume method for elliptic problems
Author(s) -
Mishev Ilya D.,
Chen QianYong
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20213
Subject(s) - discretization , mathematics , finite volume method , finite volume method for one dimensional steady state diffusion , tetrahedron , finite element method , control volume , midpoint , partial differential equation , scalar (mathematics) , mathematical analysis , geometry , numerical partial differential equations , mechanics , physics , thermodynamics
We derive a novel finite volume method for the elliptic equation, using the framework of mixed finite element methods to discretize the pressure and velocities on two different grids (covolumes), triangular (tetrahedral) mesh and control volume mesh. The new discretization is defined for tensor diffusion coefficient and well suited for heterogeneous media. When the control volumes are created by connecting the center of gravity of each triangle to the midpoints of its edges, we show that the discretization is stable and first order accurate for both scalar and vector unknowns. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007