超曲面上Laplace-Beltrami方程的Dirichlet问题-有限元逼近

IF 0.3 Q4 MATHEMATICS Transactions of A Razmadze Mathematical Institute Pub Date : 2016-12-01 DOI:10.1016/j.trmi.2016.07.003

Tengiz Buchukuri , Roland Duduchava , George Tephnadze

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摘要

本文研究了超曲面S上Laplace-Beltrami方程的Dirichlet边值问题，当曲面上的Laplace-Beltrami算子用g nter微分算子显式描述时。利用超曲面上g nter切向微分算子的演算，建立了所考虑的边值问题的有限元方法，得到了近似的显式解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dirichlet problem for Laplace–Beltrami equation on hypersurfaces—FEM approximation

We consider Dirichlet boundary value problem for Laplace–Beltrami Equation On Hypersurface $S$ , when the Laplace–Beltrami operator on the surface is described explicitly in terms of Günter’s differential operators. Using the calculus of Günter’s tangential differential operators on hypersurfaces we establish Finite Element Method for the considered boundary value problem and obtain approximate solution in explicit form.

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