Advances in Computational Mathematics
The adaptive finite element method based on multi-scale discretizations for eigenvalue problems
Computers & Mathematics with Applications
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This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on ℓ 2, the space of square summable sequences, the problem becomes sufficiently well conditioned so that a gradient type iteration can be shown to reduce the error by some fixed factor per step. It then remains to realize these (ideal) iterations within suitable dynamically updated error tolerances. It is shown under which circumstances the adaptive scheme exhibits in some sense asymptotically optimal complexity.