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Preprint 2018-11

David Mora, Iván Velásquez:

A virtual element method for the transmission eigenvalue problem

Abstract:

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 di erent families of meshes.

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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).

 

 

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