Regular convergence and finite element methods for eigenvalue problems

Regular convergence, together with other types of have been studied since the 1970s for discrete approximations linear operators. In this paper, we consider eigenvalue approximation a compact operator $T$ that can be written as an problem holomorphic Fredholm function $F(\eta) = T-\frac{1}{\eta} I$. Focusing on finite element methods (conforming, discontinuous Galerkin, non-conforming, etc.), show regular convergence functions $F_n$ to $F$ follows from operators $T_n$ $T$. The eigenvalues is then obtained using abstract theory problems functions. result used prove various such Dirichlet and biharmonic problem.