@Article{AAMM-16-636, author = {Dai , XiaoyingPan , YanYang , Bin and Zhou , Aihui}, title = {Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0099}, url = {http://global-sci.org/intro/article_detail/aamm/22932.html} }