Paper Info
Title
AFEM for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
Abstract
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.
Year
DOI
Venue
2011
10.1090/S0025-5718-2010-02435-4
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Laplace-Beltrami operator,graphs,adaptive finite element method,a posteriori error estimate,energy and geometric errors,bisection,contraction
Laplace–Beltrami operator,Polynomial,Mathematical analysis,A priori and a posteriori,Degree of a polynomial,Operator (computer programming),Numerical analysis,Mathematics,Laplace operator,Estimator
Journal
Volume
Issue
ISSN
80
274
0025-5718
Citations 
PageRank 
References 
7
0.62
10
Authors
3
Name
Order
Citations
PageRank
Khamron Mekchay1624.65
Pedro Morin233147.99
Ricardo H. Nochetto3907110.08