Finite elements on degenerate meshes: inverse-type inequalities and applications
Finite elements on degenerate meshes: inverse-type inequalities and applications
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DOI：
10.1093/imanum/drh017
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发表时间：
2005-04-01
影响因子：
2.1
通讯作者：
Sauter, SA
中科院分区：
文献类型：
--
作者：
Graham, IG;Hackbusch, W;Sauter, SA
在本文中，我们得到了一系列的反型不等式，适用于有限元函数的一般类的网格，包括退化网格各向异性加密。这些都得到了Sobolev规范的正，零和负的顺序。与经典的逆估计相比，避免了最小网格直径的负幂。我们给出了这些估计在边界元的上下文中的两个应用：（i）离散Galerkin方法中的正交误差分析和（ii）面板聚类算法的分析。我们的研究结果表明，退化的网格产生这些方法的近似性能没有退化。
In this paper we obtain a range of inverse-type inequalities which are applicable to finite-element functions on general classes of meshes, including degenerate meshes obtained by anisotropic refinement. These are obtained for Sobolev norms of positive, zero and negative order. In contrast to classical inverse estimates, negative powers of the minimum mesh diameter are avoided. We give two applications of these estimates in the context of boundary elements: (i) to the analysis of quadrature error in discrete Galerkin methods and (ii) to the analysis of the panel clustering algorithm. Our results show that degeneracy in the meshes yields no degradation in the approximation properties of these methods.