Finite element approximation of the Laplace-Beltrami operator on a surface with boundary

被引：14

作者：

Burman, Erik ^{[1
]}

Hansbo, Peter ^{[2
]}

Larson, Mats G. ^{[3
]}

Larsson, Karl ^{[3
]}

Massing, Andre ^{[3
]}

机构：

[1] UCL, Dept Math, London WC1E 6BT, England

[2] Jonkoping Univ, Dept Mech Engn, S-55111 Jonkoping, Sweden

[3] Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden

来源：

NUMERISCHE MATHEMATIK | 2019年 / 141卷 / 01期

基金：

瑞典研究理事会; 英国工程与自然科学研究理事会;

关键词：

DISCONTINUOUS GALERKIN METHOD; ELLIPTIC PROBLEMS; EQUATIONS;

D O I：

10.1007/s00211-018-0990-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order k1 in the energy and L2 norms that take the approximation of the surface and the boundary into account.

引用

页码：141 / 172

页数：32

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