LAUSR

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 $$k \ge 1$$k≥1 in the energy and $$L^2$$L2 norms that take the approximation of the surface and the boundary into account.