Nonconforming virtual element discretization for the transmission eigenvalue problem

A C0 nonconforming virtual element method (VEM) is employed for the discretization of nonselfadjoint fourth-order eigenvalue problems derived from the transmission eigenvalue problem on general polygonal meshes. Further, we linearize the model problem by introducing an auxiliary variable and thus the variational problem becomes double in size. We discretize the modified scheme by using suitable projection operators and acquire the convergence analysis under standard assumptions on the polygonal meshes. We establish that the resulting discretization provides a correct approximation of the spectrum and conclude the convergence of the eigenfunctions and eigenvalues. A variety of representative examples are examined to justify the theoretical estimates.