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

Authors

Johnny Guzman, Brown University
Alexandre Madureira, Laboratorio Nacional de Computacao Cientifica, Petropolis
Marcus Sarkis, School of Arts & Sciences
Shawn Walker, Louisiana State University

Document Type

Article

Publication Date

12-1-2018

Abstract

We derive error estimates for the piecewise linear finite element approximation of the Laplace–Beltrami operator on a bounded, orientable, C³, 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.

Publication Source (Journal or Book title)

Journal of Scientific Computing

First Page

1736

Last Page

1761

Recommended Citation

Guzman, J., Madureira, A., Sarkis, M., & Walker, S. (2018). Analysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes. Journal of Scientific Computing, 77 (3), 1736-1761. https://doi.org/10.1007/s10915-017-0580-y