Felipe Lepe, Salim Meddahi, David Mora, Rodolfo Rodríguez:
Mixed discontinuous Galerkin approximation of the elasticity eigenproblem
We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting discrete eigenproblem does not t in the standard spectral approximation framework since the underlying source operator is not compact and the scheme is nonconforming. We show that the proposed scheme provides a correct approximation of the spectrum and prove asymptotic error estimates for the eigenvalues and the eigenfunctions. Finally, we provide several numerical tests to illustrate the performance of the method and conrm the theoretical results.
This preprint gave rise to the following definitive publication(s):
Felipe LEPE, Salim MEDDAHI, David MORA, Rodolfo RODRíGUEZ: Mixed discontinuous Galerkin approximation of the elasticity eigenproblem. Numerische Mathematik, vol. 142, 3, pp. 749-786, (2019).