Analysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes

Resumo

We derive error estimates for the piecewise linear finite element approximation of the Laplace–Beltrami operator on a bounded, orientable, (Formula presented.), surface without boundary on general shape regular meshes. As an application, we consider a problem where the domain is split into two regions: one which has relatively high curvature and one that has low curvature. Using a graded mesh we prove error estimates that do not depend on the curvature on the high curvature region. Numerical experiments are provided. © 2017 Springer Science+Business Media, LLC

Ficha do documento

Tipo

Artigo científico

Ano

2017

Instituição

Springer New York LLC

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso restrito

DOI

10.1007/s10915-017-0580-y

Identificador

oai:repositorio.fgv.br:10438/25637

Palavras-chave

CurvatureFinite elementsLaplace–BeltramiLaplace transformsPiecewise linear techniquesBeltramiBeltrami equationCurvature regionsError estimatesNumerical experimentsPiecewise linearRegular meshesFinite element methodMatemáticaMétodo dos elementos finitosEquações diferenciaisLaplace, Transformadas de