Eigenvalue enclosures and convergence for the linearized MHD operator

Strauss, Michael and Boulton, Lyonell (2012) Eigenvalue enclosures and convergence for the linearized MHD operator. BIT Numerical Mathematics, 52 (4). pp. 801-825. ISSN 0006-3835

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Abstract

Computation of certified enclosures for eigenvalues of benchmark linear magnetohydrodynamics (MHD) operators in the plane slab and cylindrical pinch configuration is discussed. For the plane slab, the proposed method relies upon the formulation of an eigenvalue problem associated to the Schur complement. This leads to highly accurate upper bounds for the eigenvalue. For the cylindrical configuration, a direct application of this formulation is possible, however, it cannot be rigourously justified. Therefore in this case the proposed method relies on a specialized technique based on a method proposed by Zimmermann and Mertins. It turns out that this technique is also applicable for finding accurate complementary bounds in the case of the plane slab. Convergence rates for both approaches are established.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Michael Strauss
Date Deposited: 22 Oct 2014 10:14
Last Modified: 22 Oct 2014 10:14
URI: http://sro.sussex.ac.uk/id/eprint/50687
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