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Finite element approximation with numerical integration for differential eigenvalue problems
Institution:1. Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA;2. Department of Applied Mathematics, Financial University under the Government of the Russian Federation, Moscow 125993, Russia;3. Moscow Institute of Physics and Technology, Dolgoprudny, 141700, Russia;4. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel;1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;2. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK;1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran;2. Photonics and Nanocrystal Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran;3. School of Engineering-Emerging Technologies, University of Tabriz, Tabriz, Iran;4. Faculty of Electrical & Computer Engineering, Advanced Devices Simulation Lab, Tarbiat Modares University, Tehran 1411713116, Iran;1. College of Data Science, Jiaxing University, Jiaxing, Zhejiang 314001, China;2. College of Information Engineering, Jiaxing Nanhu University, Jiaxing, Zhejiang 314001, China
Abstract:Error estimates of the finite element method with numerical integration for differential eigenvalue problems are presented. More specifically, refined results on the eigenvalue dependence for the eigenvalue and eigenfunction errors are proved. The theoretical results are illustrated by numerical experiments for a model problem.
Keywords:Eigenvalue  Eigenfunction  Eigenvalue problem  Sturm–Liouville problem  Finite element method  Numerical integration
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