Journal of Scientific Computing

, Volume 77, Issue 3, pp 1736–1761 | Cite as

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

  • Johnny GuzmanEmail author
  • Alexandre Madureira
  • Marcus Sarkis
  • Shawn Walker


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.


Finite elements Laplace–Beltrami Curvature 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Johnny Guzman
    • 1
    Email author
  • Alexandre Madureira
    • 2
    • 3
  • Marcus Sarkis
    • 4
  • Shawn Walker
    • 5
  1. 1.Brown UniversityProvidenceUSA
  2. 2.Laboratório Nacional de Computação CientíficaPetropolisBrazil
  3. 3.Fundacao Getulio VargasRio de JaneiroBrazil
  4. 4.Mathematical Sciences DepartmentWorcester Polytechnic InstituteWorcesterUSA
  5. 5.Department of Mathematics and Center for Computation and Technology (CCT)Louisiana State UniversityBaton RougeUSA

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