Abstract
In the preceding chapters only scalar differential equations Lu = f have been considered. In the present chapter it will be pointed out that the multi-grid approach applies to elliptic systems as well. In § 11.1 we introduce examples of elliptic systems. The main difficulty of the multi-grid solution is the choice of an appropriate smoother. In § 11.2 we present a smoother which is related to the Jacobi iteration for scalar problems. A counterpart of the Gauß-Seidel iteration is the distributed relaxation described in § 11.3.
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© 1985 Springer-Verlag Berlin Heidelberg
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Hackbusch, W. (1985). Elliptic Systems. In: Multi-Grid Methods and Applications. Springer Series in Computational Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02427-0_11
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DOI: https://doi.org/10.1007/978-3-662-02427-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05722-9
Online ISBN: 978-3-662-02427-0
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