$C^0$IPG for a Fourth Order Eigenvalue Problem (Communications in Computational Physics, 2018)
This paper concerns numerical computation of a fourth order eigenvalueproblem. We first show the well-posedness of the source problem. An interior penaltydiscontinuous Galerkin method ($C^0$IPG) using Lagrange elements is proposed and itsconvergence is studied. The method is then used to compute the eigenvalues. We showthat the method is spectrally correct and prove the optimal convergence. Numericalexamples are presented to validate the theory.