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
收藏
页码：421 / 442
页数：22
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