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 - <p style="text-align: justify;">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.</p>