Mixed discontinuous Galerkin approximation of the elasticity eigenproblem

Discontinuous Galerkin approximation of the Laplace eigenproblem

In this paper we analyse the problem of computing eigenvalues and eigenfunctions of the Laplace operator by means of discontinuous Galerkin (DG) methods. It results that several DG methods actually provide a spectrally correct approximation of the Laplace operator. We present here the convergence theory, which applies to a wide class of DG methods, as well as numerical tests demonstrating the t...

Discontinuous Galerkin Approximation of the Maxwell Eigenproblem

A theoretical framework for the analysis of discontinuous Galerkin approximations of the Maxwell eigenproblem with discontinuous coefficients is presented. Necessary and sufficient conditions for a spurious-free approximation are established, and it is shown that, at least on conformal meshes, basically all the discontinuous Galerkin methods in the literature actually fit into this framework. R...

On Interior Penalty And Mixed Discontinuous Galerkin Methods For Elasticity

In this paper, we review existing discontinuous Galerkin (DG) methods for elasticity and introduce a new formulation based on mixed finite elements. We highlight the subtle and important differences between Interior Penalty (IP) and mixed FEM based methods. In the mixed method for elasticity, choices of function spaces for approximating primal and dual variable is non-trivial for two main reaso...

Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods A...

Discontinuous Galerkin methods for nonlinear elasticity