Regularity and a priori error analysis of a Ventcel problem in polyhedral domains
Regularity and a priori error analysis of a Ventcel problem in polyhedral domains
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多面体域中Ventcel问题的正则性和先验误差分析
DOI：
10.1002/mma.4083
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发表时间：
2016
影响因子：
2.9
通讯作者：
A. Mazzucato
中科院分区：
文献类型：
--
作者：
S. Nicaise;Hengguang Li;A. Mazzucato
研究了多面体区域上拉普拉斯算子的混合边值问题的正则性，其中Ventcel边界条件施加在多面体的一个面上，Dirichlet边界条件施加在该面的补面上.我们建立了改进的正则性估计的轨迹上的变分解决方案的Ventcel面，并使用它们来推导出一个分解的解决方案到一个经常和一个奇异的部分，属于合适的加权Sobolev空间。这种分解，反过来，通过插值估计在内部以及Ventcel面对，使我们能够执行一个先验误差分析的有限元近似的解决方案各向异性梯度网格。数值试验支持理论分析。版权所有© 2016约翰威利父子有限公司.
We consider the regularity of a mixed boundary value problem for the Laplace operator on a polyhedral domain, where Ventcel boundary conditions are imposed on one face of the polyhedron and Dirichlet boundary conditions are imposed on the complement of that face in the boundary. We establish improved regularity estimates for the trace of the variational solution on the Ventcel face and use them to derive a decomposition of the solution into a regular and a singular part that belongs to suitable weighted Sobolev spaces. This decomposition, in turn, via interpolation estimates both in the interior as well as on the Ventcel face, allows us to perform an a priori error analysis for the finite element approximation of the solution on anisotropic graded meshes. Numerical tests support the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd.