Finite element approximation of the Laplace–Beltrami operator on a surface with boundary

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 [Formula: see text] in the energy and [Formula: see text] norms that take the approximation of the surface and the boundary into account.