CONVERGENCE OF MULTI-POINT FLUX APPROXIMATIONS ON GENERAL GRIDS AND MEDIA
CONVERGENCE OF MULTI-POINT FLUX APPROXIMATIONS ON GENERAL GRIDS AND MEDIA
复制标题
一般网格和介质上多点通量近似的收敛性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Stephansen
中科院分区：
文献类型：
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作者：
R. A. Klausen;A. Stephansen
多点通量近似（MPFA）方法的分析，到目前为止，依赖于将其视为混合有限元方法，然后建立收敛的可能性。这种类型的分析已成功地应用于三角形和四边形，也在粗糙网格的情况下。然而，MPFA方法与另一种众所周知的保守方法：模拟有限差分法有很多共同之处。我们建议制定的MPFA O-方法在一个模仿有限差分框架，以扩大证明的收敛性多面体网格。该公式有助于了解两种不同方法之间的密切关系，并了解差异如何导致不同的强度。我们特别注意在数值测试部分中通过检查各种情况来证明收敛性所需的假设。
The analysis of the Multi Point Flux Approximation (MPFA) method has so far relied on the possibility of seeing it as a mixed finite element method for which the convergence is then established. This type of analysis has been successfully applied to triangles and quadrilaterals, also in the case of rough meshes. The MPFA method has however much in common with another well known conservative method: the mimetic finite difference method. We propose to formulate the MPFA O-method in a mimetic finite difference framework, in order to extend the proof of convergence to polyhedral meshes. The formulation is useful to see the close relationship between the two different methods and to see how the differences lead to different strenghts. We pay special attention to the assumption needed for proving convergence by examining various cases in the section dedicated to numerical tests.