Mixed discontinuous Galerkin approximation of the elasticity eigenproblem
This work provides a theoretical and numerical framework for approximating eigenvalues in elasticity problems using a nonconforming mixed DG method, addressing a gap in spectral approximation theory.
The authors develop a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry, proving asymptotic error estimates for eigenvalues and eigenfunctions, and confirming results with numerical tests.
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 fit 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 confirm the theoretical results.