TY - JOUR T1 - Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations AU - Dai , Xiaoying AU - Pan , Yan AU - Yang , Bin AU - Zhou , Aihui JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 636 EP - 666 PY - 2024 DA - 2024/02 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0099 UR - https://global-sci.org/intro/article_detail/aamm/22932.html KW - Adaptive planewave method, convergence rate, complexity, eigenvalue. AB -

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.