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Gruber R., Rappaz J. Finite element methods in linear ideal magnetohydrodynamics

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Gruber R., Rappaz J. Finite element methods in linear ideal magnetohydrodynamics
Springer –Verlag, Berlin, Heidelberg, 1985. – 189 pp. (Springer Series in Computational Physics).
For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called "spectral pollution" appeared. We were able to eliminate it by our "ecological solution". This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the "finite hybrid elements". These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construction, testing and using of our stability code ERATO. We would like to thank them here.
Contents.
Introduction.
Finite Element Methods for the Discretization of Differential Eigenvalue Problems.
The Ideal MHD Model.
Cylindrical Geometry.
Two-Dimensional Finite Elements Applied to Cylindrical Geometry.
ERATO: Application to Toroidal Geometry.
HERA: Application to Helical Geometry (Peter Merkei, IPP Garehing).
Similar Problems.
Appendices.
References.
Subject Index.
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