Year: 2024
Author: Xiaoying Dai, Yan Pan, Bin Yang, Aihui Zhou
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 3 : pp. 636–666
Abstract
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0099
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 3 : pp. 636–666
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Adaptive planewave method convergence rate complexity eigenvalue.