多面体域中Ventcel问题的正则性及先验误差分析
Regularity and a priori error analysis of a Ventcel problem in polyhedral domains
AI总结：
本文研究了多面体域中Laplace算子混合边界值问题的正则性及有限元近似误差分析，通过分解解为正则和奇异部分，利用插值估计在域内和Ventcel面上进行先验误差分析。
摘要：
我们考虑了在多面体域上Laplace算子的混合边界值问题的正则性，其中Ventcel边界条件施加于多面体的一个面上，而Dirichlet边界条件施加于该面其余部分。我们建立了变分解在Ventcel面上的迹的改进正则性估计，并利用这些估计将解分解为属于合适加权Sobolev空间的正则部分和奇异部分。这种分解通过域内及Ventcel面上的插值估计，使得能够在各向异性分层网格上进行有限元近似解的先验误差分析。数值测试支持了理论分析。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
