This paper introduces bootstrap two-grid and multigrid finite element
approximations to the Laplace-Beltrami (surface Laplacian) eigen-problem on a
closed surface. The proposed multigrid method is suitable for recovering
eigenvalues having large multiplicity, computing interior eigenvalues, and
approximating the shifted indefinite eigen-problem. Convergence analysis is
carried out for a simplified two-grid algorithm and numerical experiments are
presented to illustrate the basic components and ideas behind the overall
bootstrap multigrid approach