期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 50, 期 3, 页码 1029-1057出版社
SIAM PUBLICATIONS
DOI: 10.1137/090769430
关键词
eigenvalue; adaptive finite element method; convergence rates; complexity
资金
- German Research Foundation (DFG) in the Research Center Matheon Mathematics for Key Technologies
- World Class University (WCU) program through the National Research Foundation of Korea (NRF)
- Ministry of Education, Science, and Technology [R31-2008-000-10049-0]
- graduate school Berlin Mathematical School (BMS)
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.
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