Adv. Appl. Math. Mech., 16 (2024), pp. 636-666.
Published online: 2024-02
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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} }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.