Preprint 2020-18
David Mora, Iván Velásquez:
Virtual elements for the transmission eigenvalue problem on polytopal meshes
Abstract:
The transmission eigenvalue problem is a challenging model in the inverse scattering theory and has important applications in this topic. The aim of this paper is to analyze a $C^1$ Virtual Element Method (VEM) on polytopal meshes in $\R^d$ $(d=2,3)$ for solving a quadratic and non-self-adjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory for compact non-self-adjoint operators. Finally, a set of numerical tests illustrating the good performance of the virtual scheme are presented.
This preprint gave rise to the following definitive publication(s):
David MORA, Iván VELáSQUEZ: Virtual elements for the transmission eigenvalue problem on polytopal meshes. SIAM Journal on Scientific Computing, vol. 43, 4, pp. A2425-A2447, (2021).