An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces

被引：116

作者：

Demlow, Alan

Dziuk, Gerhard

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] Abt Angew Math, D-79104 Freiburg, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2007年 / 45卷 / 01期

关键词：

Laplace-Beltrami operator; adaptive finite element methods; a posteriori error estimation; boundary value problems on surfaces;

D O I：

10.1137/050642873

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in R-3 which may be implicitly represented as level sets of smooth functions. Residual-type a posteriori error bounds which show that the error may be split into a "residual part" and a "geometric part" are established. In addition, implementation issues are discussed and several computational examples are given.

引用

页码：421 / 442

页数：22

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