A Holomorphic Operator Function Approach for the Laplace Eigenvalue Problem Using Discontinuous Galerkin Method (CSIAM Transactions on Applied Mathematics, 2021)
The paper presents a holomorphic operator function approach for the Laplaceeigenvalue problem using the discontinuous Galerkin method. We rewrite the problem as the eigenvalue problem of a holomorphic Fredholm operator function of indexzero. The convergence for the discontinuous Galerkin method is proved by using theabstract approximation theory for holomorphic operator functions. We employ thespectral indicator method to compute the eigenvalues. Extensive numerical examplesare presented to validate the theory.
Keywords: Discontinuous Galerkin method; eigenvalue problem; Fredholm operator.