Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations
Numerical Analysis
2022-10-28 v2 Numerical Analysis
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.
Cite
@article{arxiv.2106.01008,
title = {Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations},
author = {Xiaoying Dai and Yan Pan and Bin Yang and Aihui Zhou},
journal= {arXiv preprint arXiv:2106.01008},
year = {2022}
}
Comments
29 pages