A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
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DOI：
10.1007/s00211-011-0427-7
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发表时间：
2011-11
影响因子：
2.1
通讯作者：
M. Wheeler;Guangri Xue;I. Yotov
中科院分区：
文献类型：
--
作者：
M. Wheeler;Guangri Xue;I. Yotov
本文提出了一种新的四边形和六面体网格上椭圆型问题的混合有限元方法，该方法可简化为以胞为中心的有限差分格式。采用了一种特殊的非对称正交规则，通过消除局地速度，得到一个正的胞心压力系统。该方法在高度变形的粗糙四边形和六面体网格（包括具有非平面面的六面体）上具有较好的精度。理论和数值结果表明压力通量和工作面通量具有一阶收敛性。
In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes.