# zbMATH — the first resource for mathematics

Tunable integration scheme for the finite element method. (English) Zbl 1031.76554
Summary: A discretization method is proposed where a tunable integration scheme is applied to the finite element method (FEM). The method is characterized by one continuous parameter, $$p$$. A theoretical error analysis is given and three different eigenvalue problems are used as test cases: a simple example with constant coefficients and two model problems from ideal and resistive magnetohydrodynamics. It is shown that, for judicious choices of $$p$$, the tunable integration method clearly improves the convergence of the strict FEM. The sensitivity to the choice of integration parameter is discussed.

##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 76M10 Finite element methods applied to problems in fluid mechanics
ERATO
Full Text:
##### References:
 [1] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, NJ · Zbl 0278.65116 [2] Hughes, T.J.R., The finite element method, (1987), Prentice-Hall Englewood Cliffs, NJ [3] Appert, K.; Berger, D.; Gruber, R.; Troyon, F.; Rappaz, J., Z. angew. math. phys., 25, 229, (1974) [4] Llobet, X.; Appert, K.; Bondeson, A.; Vaclavik, J., Comput. phys. commun., 59, 199, (1990) [5] Richtmyer, R.D.; Morton, K.W., Difference methods for initial value problems, (1967), Interscience New York · Zbl 0155.47502 [6] Gruber, R., Comput. phys. commun., 21, 323, (1981) [7] Newcomb, W.A., Ann. phys., 10, 232, (1960) [8] Suydam, B.R., (), 157 [9] Mercier, C., Nucl. fusion, 1, 47, (1960) [10] Degtyarev, L.M.; Medvedev, S.Yu., Comput. phys commun., 43, 29, (1986) [11] Cooper, W.A.; Fu, G.Y.; Gruber, R.; Merazzi, S.; Schwenn, U.; Anderson, D., Theory of fusion plasmas, (), 665 [12] Coppi, B.; Greene, J.M.; Johnson, J.L., Nucl. fusion, 6, 101, (1966) [13] Bondeson, A.; Vlad, G.; Lütjens, H., Controlled fusion and plasma physics, (), 906, Part II
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.