A MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD ON HEXAHEDRA

被引：59
作者：
Ingram, Ross [1 ]
Wheeler, Mary F. [2 ]
Yotov, Ivan [1 ]
机构：
[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
[2] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 04期
基金：
美国国家科学基金会;
关键词：
mixed finite element; multipoint flux approximation; cell-centered finite difference; tensor coefficient; error estimates; hexahedra; QUADRILATERAL GRIDS; ELLIPTIC PROBLEMS; DIFFUSION-PROBLEMS; DIFFERENCE METHOD; POLYHEDRAL MESHES; VOLUME METHODS; CONVERGENCE; DISCRETIZATION; APPROXIMATIONS; SUPERCONVERGENCE;
D O I：
10.1137/090766176
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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-Duran-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.
引用
收藏
页码：1281 / 1312
页数：32
相关论文
共 49 条
[1]   Convergence of a symmetric MPFA method on quadrilateral grids [J].
Aavatsmark, I. ;
Eigestad, G. T. ;
Klausen, R. A. ;
Wheeler, M. F. ;
Yotov, I. .
COMPUTATIONAL GEOSCIENCES, 2007, 11 (04) :333-345
[2]   Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods [J].
Aavatsmark, I ;
Barkve, T ;
Boe, O ;
Mannseth, T .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 19 (05) :1700-1716
[3]   An introduction to multipoint flux approximations for quadrilateral grids [J].
Aavatsmark, I .
COMPUTATIONAL GEOSCIENCES, 2002, 6 (3-4) :405-432
[4]  
[Anonymous], 2002, MATH THEORY FINITE E, DOI DOI 10.1007/978-1-4757-3658-8
[5]  
[Anonymous], 1971, Approximate Calculation of Multiple Integrals
[6]  
[Anonymous], 1991, SPRINGER SER COMPUT
[7]  
[Anonymous], 1994, An introduction to the mathematical theory of the Navier-Stokes equations
[8]  
[Anonymous], 1977, MATH ASPECTS FINITE
[9]  
Arbogast T, 1998, SIAM J SCI COMPUT, V19, P404, DOI 10.1137/S1064827594264545
[10]   Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences [J].
Arbogast, T ;
Wheeler, MF ;
Yotov, I .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (02) :828-852
12345