Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we study the adaptive planewave discretization for a clusterof eigenvalues of second-order elliptic partial differential equations. We first designan a posteriori error estimator and prove both the upper and lower bounds. Based onthe a posteriori error estimator, we propose an adaptive planewave method. We thenprove that the adaptive planewave approximations have the linear convergence rateand quasi-optimal complexity.