A Multipoint Flux Mixed Finite Element Method
A Multipoint Flux Mixed Finite Element Method
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DOI：
10.1137/050638473
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发表时间：
2006-09
期刊：
影响因子：
--
通讯作者：
M. Wheeler;I. Yotov
中科院分区：
文献类型：
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作者：
M. Wheeler;I. Yotov
我们发展了一种求解多孔介质中单相流动的混合有限元方法，该方法在四边形和单纯形网格上简化为以单元为中心的有限差分，并对不连续的全张量系数具有很好的性能。受引入Subedge通量的多点通量近似方法的启发，我们考虑了最低阶Brezzi-Douglas-Marini(BDM)混合有限元方法。采用了一种特殊的求积规则，允许局部速度消除，并导致压力的对称和正定的胞心系统。理论和数值结果表明，胞心压力的二阶收敛和Subedge通量的一阶收敛。当网格足够规则时，边界通量的二阶收敛也可以通过计算观察到。
We develop a mixed finite element method for single phase flow in porous media that reduces to cell-centered finite differences on quadrilateral and simplicial grids and performs well for discontinuous full tensor coefficients. Motivated by the multipoint flux approximation method where subedge fluxes are introduced, we consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method. 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 second-order convergence for pressures at the cell centers and first-order convergence for subedge fluxes. Second-order convergence for edge fluxes is also observed computationally if the grids are sufficiently regular.