The multigrid discretization of mixed discontinuous Galerkin method for the biharmonic eigenvalue problem

The Ciarlet-Raviart mixed method is popular for the biharmonic equations/eigenvalue problem. In this paper, we propose a multigrid discretization based on the shifted-inverse iteration of Ciarlet-Raviart mixed discontinuous Galerkin method for the biharmonic eigenvalue problem. We prove the a priori error estimates of the approximate eigenpairs. We also give the a posteriori error estimates of the approximate eigenvalues and prove the reliability of the estimator and implement adaptive computation. Numerical experiments show that our method can efficiently compute biharmonic eigenvalues.