Finite Element Approximation of the Laplace-Beltrami Operator on a Surface with Boundary

Abstract

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order $k\ge 1$ in the energy and $L^2$ norms that take the approximation of the surface and the boundary into account.

29 pages, 6 figures

References in corpus (2)

• Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
• A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces

Cited by in corpus (2)

• Surface Crouzeix-Raviart element for the Laplace-Beltrami equation
• Hybridized Isogeometric Method for Elliptic Problems on CAD Surfaces with Gaps