AFEM FOR THE LAPLACE-BELTRAMI OPERATOR ON GRAPHS: DESIGN AND CONDITIONAL CONTRACTION PROPERTY

被引：17

作者：

Mekchay, Khamron ^{[1
]}

Morin, Pedro ^{[2
]}

Nochetto, Ricardo H. ^{[3
,4
]}

机构：

[1] Chulalongkorn Univ, Dept Math, Fac Sci, Bangkok 10330, Thailand

[2] Univ Nacl Litoral, Inst Matemat Aplicada Litoral, CONICET, RA-3450 Guemes, Santa Fe, Argentina

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[4] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

来源：

MATHEMATICS OF COMPUTATION | 2011年 / 80卷 / 274期

关键词：

Laplace-Beltrami operator; graphs; adaptive finite element method; a posteriori error estimate; energy and geometric errors; bisection; contraction; FINITE-ELEMENT METHODS; ELLIPTIC PROBLEMS; CONVERGENCE;

D O I：

10.1090/S0025-5718-2010-02435-4

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 (AFEM) of any polynomial degree for the Laplace-Beltrami operator on C-1 graphs Gamma in R-d (d >= 2). We first derive residual-type a posteriori error estimates that account for the interaction of both the energy error in H-1(Gamma) and the surface error in W-infinity(1)(Gamma) due to approximation of P. We devise a marking strategy to reduce the total error estimator, namely a suitably scaled sum of the energy, geometric, and inconsistency error estimators. We prove a conditional contraction property for the sum of the energy error and the total estimator; the conditional statement encodes resolution of Gamma in W-infinity(1) We conclude with one numerical experiment that illustrates the theory.

引用

页码：625 / 648

页数：24

共 21 条

[1]

Ainsworth M., 2000, PUR AP M-WI

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