Analysis of finite element methods for surface vector-Laplace eigenproblems

In this paper we study finite element discretizations of a surface vector-Laplace eigenproblem. We consider two known classes methods, namely one based on vector analogon the Dziuk-Elliott method and so-called trace technique. A key ingredient in both methods is penalization that used to enforce tangentiality field weak sense. This perturbations arise from numerical approximation lead essential nonconformities discretization variational formulation present general abstract framework applicable such nonconforming eigenproblems. Error bounds for eigenvalue eigenvector approximations are derived depend certain consistency approximability parameters. Sharpness these discussed. Results experiment illustrate convergence properties