Finite element analysis of an eigenvalue problem arising from neutron transport

In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a standard finite element approximation based on piecewise polynomials of degree $k \geq 1$, and under the framework of the compact operators theory, we prove convergence and error estimates of the proposed method. We report a series of numerical tests in order confirm the theoretical results.