  A numerical scheme to compute the spectrum of a large class of self-adjoint
extensions of the Laplace-Beltrami operator on manifolds with boundary in any
dimension is presented. The algorithm is based on the characterisation of a
large class of self-adjoint extensions of Laplace-Beltrami operators in terms
of their associated quadratic forms. The convergence of the scheme is proved. A
two-dimensional version of the algorithm is implemented effectively and several
numerical examples are computed showing that the algorithm treats in a unified
way a wide variety of boundary conditions.
