Bootstrap Multigrid for the Laplace-Beltrami Eigenvalue Problem

This paper introduces bootstrap two-grid and multigrid finite element approximations to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface. The proposed multigrid method is suitable for recovering eigenvalues having large multiplicity, computing interior eigenvalues, and approximating the shifted indefinite eigen-problem. Convergence analysis is carried out for a simplified two-grid algorithm and numerical experiments are presented to illustrate the basic components and ideas behind the overall bootstrap multigrid approach

An Interior Penalty Method with C0C^0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

The present paper proposes and analyzes an interior penalty technique using $C^0$-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally correct.Comment: 36 page