## Numerical methods for spectral problems: theory and applications

P000019

### Multigrid method for linear and nonlinear eigenvalue problems

*Hehu Xie (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

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 Related papers 1. Qun Lin and Hehu Xie, An observation on Aubin-Nitsche Lemma and its applications, Mathematics in Practice and Theory, 41(17) (2011), 247-258.(In Chinese, English title and abstract) 2. Hehu Xie, A multigrid method for eigenvalue problem, Journal of Computational Physics, 274(1), 2014, pages 550-561. 3. Hehu Xie, A type of multilevel method for the Steklov eigenvalue problem, IMA J. Numer. Anal., 34(2) (2014), 592-608. 4. Qun Lin and Hehu Xie, A multi-level correction scheme for eigenvalue problems, Mathematics of Computation, 84(291) (2015), 71-88. 5. Hehu Xie, A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods, BIT Numerical Mathematics, 55(4) (2015), 1243-1266. 6. Hehu Xie and Manting Xie, A multigrid method for ground state solution of Bose-Einetein condensates, Commun. Comput. Phys., 19(3) (2016), 648-662. 7.Guanghui Hu, Hehu Xie and Fei Xu, A multilevel correction adaptive finite element method for Kohn–Sham equation, Journal of Computational Physics, 355 (2018), 436-449. 8. Qichen Hong, Hehu Xie and Fei Xu, A Multilevel Correction Type of Adaptive Finite Element Method for Eigenvalue Problems, SIAM J. Sci. Comput., 40(6) (2018), A4208–A4235. Keywords Eigenvalue problem, multilevel correction, multigrid method