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- Title
A virtual element method for the transmission eigenvalue problem.
- Authors
Mora, David; Velásquez, Iván
- Abstract
In this paper, we analyze a Virtual Element Method (VEM) for solving a non-self-adjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a C 1 -conforming discretization by means of the VEM. We use the classical approximation theory for compact non-self-adjoint 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 different families of meshes.
- Subjects
NONSELFADJOINT operators; EIGENVALUES; DISCRETIZATION methods; APPROXIMATION theory; EIGENFUNCTIONS
- Publication
Mathematical Models & Methods in Applied Sciences, 2018, Vol 28, Issue 14, p2803
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202518500616