A MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD ON HEXAHEDRA

We develop a mixed finite element method for elliptic problems on hexahedral grids that reduces to cell-centered finite differences. The paper is an extension of our earlier paper for quadrilateral and simplicial grids [M. F. Wheeler and I. Yotov, SIAM J. Numer. Anal, 44 (2006), pp. 2082-2106]. The...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2010-01, Vol.48 (4), p.1281-1312
Main Authors: INGRAM, ROSS, WHEELER, MARY F., YOTOV, IVAN
Format: Article
Language:English
Subjects:
Approximation
Coefficients
Convergence
Degrees of freedom
Error analysis
Error rates
Finite element analysis
Finite element method
Flux
Fluxes
Mathematical analysis
Mathematical vectors
Numerical analysis
Parallelepipeds
Quadratures
Statistical analysis
Studies
Tensors
Vertices
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Summary:We develop a mixed finite element method for elliptic problems on hexahedral grids that reduces to cell-centered finite differences. The paper is an extension of our earlier paper for quadrilateral and simplicial grids [M. F. Wheeler and I. Yotov, SIAM J. Numer. Anal, 44 (2006), pp. 2082-2106]. The construction is motivated by the multipoint flux approximation method, and it is based on an enhancement of the lowest order Brezzi-Douglas-Durán-Fortin (BDDF) mixed finite element spaces on hexahedra. In particular, there are four fluxes per face, one associated with each vertex. A special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell-centered system for the pressures. Theoretical and numerical results indicate first-order convergence for pressures and subface fluxes on sufficiently regular grids, as well as second-order convergence for pressures at the cell centers. Second-order convergence for face fluxes is also observed computationally.
ISSN:0036-1429
1095-7170
DOI:10.1137/090766176