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

This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for the Laplace eigenvalue problem of 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 k>0. The 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 optimal computational complexity.

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