David Mora, Iván Velásquez:
A virtual element method for the transmission eigenvalue problem
In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourthorder eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a C1-conforming discretization by means of the VEM.We use the classical approximation theory for compact non-selfadjoint operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues. Finally, we present some numerical experiments illustrating the behavior of the virtual scheme on dierent families of meshes.
This preprint gave rise to the following definitive publication(s):
David MORA, Iván VELáSQUEZ: A virtual element method for the transmission eigenvalue problem. Mathematical Models and Methods in Applied Sciences, vol. 28, 14, pp. 2803-2831, (2018).