A New Method using C IPG for the Biharmonic Eigenvalue Problem

The paper presents a new proof of the CIPG method (C interior penalty Galerkin method) for the biharmonic eigenvalue problem. Instead of using the proof following the structure of discontinuous Galerkin method, we rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for CIPG is proved using the abstract approximation theory for holomorphic operator functions. We employ the spectral indicator method which is easy in coding to compute the eigenvalues. Numerical examples are presented to validate the theory.