Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity
Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity
复制标题
线弹性的单元中心有限体积离散化的收敛性
DOI：
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发表时间：
2015
影响因子：
2.9
通讯作者：
J. Nordbotten
中科院分区：
文献类型：
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作者：
J. Nordbotten
我们显示收敛的一个细胞为中心的有限体积离散线弹性。离散化，称为MPSA方法，最近提出的地质应用的背景下，细胞为中心的变量往往是首选。我们的分析利用了混合变分制剂，这是以前被用来分析标量扩散方程的有限体积离散。目前的分析在三个方面与以前的分析有很大的不同。首先，额外的稳定导致一个更复杂的鞍点问题。其次，离散的Korn不等式必须建立的全球离散化。最后，相对于泊松比的鲁棒性进行了分析。本文给出的稳定性和收敛性的结果提供了第一个严格的理由的适用性的格心有限体积法的问题，在线性弹性。
We show convergence of a cell-centered finite volume discretization for linear elasticity. The discretization, termed the MPSA method, was recently proposed in the context of geological applications, where cell-centered variables are often preferred. Our analysis utilizes a hybrid variational formulation, which has previously been used to analyze finite volume discretizations for the scalar diffusion equation. The current analysis deviates significantly from the previous in three respects. First, additional stabilization leads to a more complex saddle-point problem. Second, a discrete Korn's inequality has to be established for the global discretization. Finally, robustness with respect to the Poisson ratio is analyzed. The stability and convergence results presented herein provide the first rigorous justification of the applicability of cell-centered finite volume methods to problems in linear elasticity.