Conservative flux recovery from the Q1 conforming finite element method on quadrilateral grids
Conservative flux recovery from the Q1 conforming finite element method on quadrilateral grids
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DOI：
10.1002/num.10084
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发表时间：
2004-01
影响因子：
3.9
通讯作者：
S. Chou;Songnian He;Wen Lin
中科院分区：
文献类型：
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作者：
S. Chou;Songnian He;Wen Lin
与标准Galerkin有限元方法相比，二阶椭圆问题的混合方法提供了容易获得的通量近似，但通常以必须处理更复杂的离散系统为代价。当涉及一致性元素时尤其如此。因此，当发现通量只是整个建模过程的一小部分时，考虑直接方法是有利的。本文的目的是介绍一种将标准Galerkin Q1协调方法与廉价的局部通量恢复公式相结合的直接方法。近似通量位于最低阶Raviart-托马斯空间中，并在簇水平上保持局部守恒性质。一个簇最多由四个四边形组成。© 2004 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 20：104-127，2004
Compared with standard Galerkin finite element methods, mixed methods for second‐order elliptic problems give readily available flux approximation, but in general at the expense of having to deal with a more complicated discrete system. This is especially true when conforming elements are involved. Hence it is advantageous to consider a direct method when finding fluxes is just a small part of the overall modeling processes. The purpose of this article is to introduce a direct method combining the standard Galerkin Q1 conforming method with a cheap local flux recovery formula. The approximate flux resides in the lowest order Raviart‐Thomas space and retains local conservation property at the cluster level. A cluster is made up of at most four quadrilaterals. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 104–127, 2004