Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes

Autor:	Guzman, Johnny, Madureira, Alexandre, Sarkis, Marcus, Walker, Shawn
Rok vydání:	2017
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, $C^3$, 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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1705.04369 Zobrazit plný text záznamu View this record from Arxiv