Numerical approximation of the spectrum of the curl operator

Rodríguez, Rodolfo; Venegas, Pablo

doi:10.1090/S0025-5718-2013-02745-7

Numerical approximation of the spectrum of the curl operator
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by Rodolfo Rodríguez and Pablo Venegas PDF

Math. Comp. 83 (2014), 553-577 Request permission

Abstract:

The aim of this paper is to study the numerical approximation of the eigenvalue problem for the curl operator. The three-dimensional divergence-free eigensolutions of this problem are examples of the so-called Beltrami fields or linear force-free fields, which arise in various physics areas such as solar physics, plasma physics, and fluid mechanics. The present analysis is restricted to bounded simply-connected domains. Finite element discretizations of two weak formulations of the spectral problem are proposed and analyzed. Optimal-order spectral convergence is proved, as well as absence of spurious modes. The results of some numerical tests are also reported.

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