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arXiv · 1509.08597

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

E. Burman·P. Hansbo·M. G. Larson·K. Larsson·A. Massing
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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 $k \geq 1$ in the energy and $L^2$ norms that take the approximation of the surface and the boundary into account.

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E. Burman, P. Hansbo, M. G. Larson, K. Larsson, A. Massing. 2015-09-29. Finite Element Approximation of the Laplace-Beltrami Operator on a Surface with Boundary. https://doi.org/10.1007/s00211-018-0990-2

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