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Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations (2106.01008v2)
Published 2 Jun 2021 in math.NA and cs.NA
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.
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