主 题: CAM Seminar——Adaptive Eigenvalue Computation
报告人: Prof. C. Carstensen (Humboldt University)
时 间: 2018-01-03 16:00-17:00
地 点: Room 1479, Sciences Buildin No. 1
Abstract: This talk presents recent advances in the nonconforming FEM approximation of elliptic PDE eigenvalue problems. The first part introduces guaranteed lower eigenvalue bounds for second-order and fourth-order eigenvalue problems with relevant applications for the localization of in the critical load in the buckling analysis of the Kirchhoff plates. The second studies an optimal adaptive mesh-refining algorithm for the effective eigenvalue computation for the Laplace operator with optimal convergence rates in terms of the number of degrees of freedom relative to the concept of nonlinear approximation classes. The analysis includes an inexact algebraic eigenvalue computation on each level of the adaptive algorithm which requires an iterative algorithm and a controlled termination criterion. The third part extends the analysis to multiple and even clustered eigenvalues. The topics reflect joint work with Dr Joscha Gedike (Vienna) and Dr Dietmar Gallistl (KIT).
[1] C. Carstensen and D. Gallistl, Guaranteed lower eigenvalue bounds for the biharmonic equation, Numer. Math. 126 (2014)
[2] C. Carstensen, D. Gallistl, M. Schedensack, Discrete reliability for CrouzeixRaviart FEMs SINUM 51(5), 2013
[3] C. Carstensen, D. Gallistl, M. Schedensack, Adaptive nonconforming CrouzeixRaviart FEM for eigenvalue problems Math. Comp. 84(293), 2015
[4] C. Carstensen, J. Gedicke, An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity SINUM 50(3) 2012
[5] C. Carstensen, J. Gedicke, Guaranteed lower bounds for eigenvalues, Math. Comp. 83(290) 2014
[6] D. Gallistl, An optimal adaptive FEM for eigenvalue clusters Numer. Math. 130(3) 2015
[7] D. Gallistl, Adaptive nonconforming finite element approximation of eigenvalue clusters Comput. Methods Appl. Math.14(4) 2014
[8] D. Gallistl, Morley finite element method for the eigenvalues of the biharmonic operator IMA J. Numer. Anal. 35(4) 2015
