An Adaptive Finite Element Eigenvalue Solver of Asymptotic Quasi-Optimal Computational Complexity

This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal computational complexity. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher-order conforming finite element spaces with fixed polynomial degree. The asymptotic quasi-optimal adaptive finite element eigenvalue solver (AFEMES) involves a proper termination criterion for the algebraic eigenvalue solver and does not need any coarsening. Numerical evidence illustrates the asymptotic quasi-optimal computational complexity in 2 and 3 dimensions.