Lütjens, H.; Luciani, J. F. A class of basis functions for non-ideal magnetohydrodynamic computations. (English) Zbl 0923.76207 Comput. Phys. Commun. 95, No. 1, 47-57 (1996). Summary: A new spatial discretization method of the magnetohydrodynamic (MHD) stability problem is presented. This method ensures that the linearized discretized problem remains exactly variational in the limit of ideal MHD. It is shown with a one-dimensional model equation that this new method eliminates a class of numerical modes existing with previous discretization methods. Improvements in the convergence properties are presented in ideal and resistive MHD. Cited in 1 Document MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76W05 Magnetohydrodynamics and electrohydrodynamics Keywords:magnetohydrodynamic stability; convergence; resistive MHD Software:ERATO PDF BibTeX XML Cite \textit{H. Lütjens} and \textit{J. F. Luciani}, Comput. Phys. Commun. 95, No. 1, 47--57 (1996; Zbl 0923.76207) Full Text: DOI References: [1] Appert, K.; Berger, D.; Gruber, R.; Troyon, F.; Rappaz, J., Z. ang. math. phys., 25, 229, (1974) [2] Appert, K.; Berger, D.; Gruber, R.; Rappaz, J., J. comput. phys., 18, 284, (1975) [3] Gruber, R., J. comput. phys., 26, 379, (1978) [4] Gruber, R.; Troyon, F.; Berger, D.; Bernard, L.C.; Rousset, S.; Schreiber, R.; Kerner, W.; Schneider, W.; Roberts, K.V., Comput. phys. commun., 21, 323, (1981) [5] Bondeson, A.; Vlad, G.; Lütjens, H., Phys. fluids B, 4, 1889, (1992) [6] Lerbinger, K.; Luciani, J.F., J. comput. phys., 97, 444, (1991) [7] Suydam, B.R., (), 157 [8] Mercier, C., Nucl. fusion suppl., 1, 47, (1960) [9] Degtyarev, L.M.; Medvedev, S.Y., Comput. phys. commun., 43, 29, (1986) [10] D.V. Anderson, A. Cooper, U. Schwenn and R. Gruber, Theory of Fusion Plasmas 1988, Proc. of the Joint Varenna-Lausanne International Workshop, Chexbres, Switzerland, p. 93. [11] Fu, G.Y.; Cooper, W.A.; Gruber, R.; Schwenn, U.; Anderson, D.V., Phys. fluids B, 4, 1401, (1992) [12] Bondeson, A.; Fu, G.Y., Comput. phys. commun., 66, 167, (1991) [13] Coppi, B.; Greene, J.M.; Johnson, J.L., Nucl. fusion, 6, 101, (1966) [14] Newcomb, W.A., Ann. phys., 10, 232, (1960) [15] Strang, G.; Fix, G., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, NJ, Ch. 6.1 · Zbl 0278.65116 [16] Fletcher, C.A.J., (), Ch. 7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.