We design an adaptive procedure for approximating a selected eigenvalue and its eigen-space for a second-order elliptic boundary-value problem, using an hp finite element method. Such iterative procedure judiciously alternates between a stage in which a near-optimal hp-mesh for the current level of accuracy is generated, and a stage in which such mesh is sufficiently refined to produce a new, enhanced approximation of the eigenfunctions. We identify conditions on the initial mesh and the operator coefficients under which the procedure yields approximations that converge at a geometric rate independent of any discretization parameter, using a number of degrees of freedom comparable to the smallest number needed to get the achieved accuracy. We detail the second stage for a single eigenvalue, relying on a p-robust saturation property.
Adaptive hp -FEM for eigenvalue computations / Canuto, C.. - In: CALCOLO. - ISSN 0008-0624. - ELETTRONICO. - 56:4(2019), p. 39. [10.1007/s10092-019-0335-2]
Titolo: | Adaptive hp -FEM for eigenvalue computations | |
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Data di pubblicazione: | 2019 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10092-019-0335-2 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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hpAFEM-EIG.pdf | Articolo principale | 1. Preprint / submitted version [pre- review] | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
Canuto2019_Article_AdaptiveMathbfHpHp-FEMForEigen.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2794312