Adaptive hp -FEM for eigenvalue computations

Canuto, C.

doi:10.1007/s10092-019-0335-2

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
Autori:	CANUTO, CLAUDIO
Data di pubblicazione:	2019
Rivista:	CALCOLO
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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