Preprint 2021-21
David Mora, Iván Velásquez:
A $C^{1}-C^{0}$ conforming virtual element discretization for the transmission eigenvalue problem
Abstract:
In this study, we present and analyze a virtual element discretization for a non-selfadjoint fourth order eigenvalue problem derived from the transmission eigenvalue problem. Using suitable projection operators, the sesquilinear forms are discretized by only using the proposed degrees of freedom associated with the virtual spaces. Under standard assumptions on the polygonal meshes, we show that the resulting scheme provides a correct approximation of the spectrum and prove an optimal order error estimate for the eigenfunctions and a double order for the eigenvalues. Finally, we present some numerical experiments illustrating the behavior of the virtual scheme on different families of meshes.
This preprint gave rise to the following definitive publication(s):
David MORA, Iván VELáSQUEZ: A $C^{1}-C^{0}$ conforming virtual element discretization for the transmission eigenvalue problem. Research in the Mathematical Sciences, vol. 8, 4, Paper No. 56, 21 pp., (2021).