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Zbl 0974.65113
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
Multigrid in H(div) and H(curl). (English)
[J] Numer. Math. 85, No.2, 197-217 (2000). ISSN 0029-599X; ISSN 0945-3245/e

The authors are concerned with multigrid methods for 3D variational problems in the Hilbert spaces H(div) and H(curl) which naturally arise in problems of continuum mechanics and electromagnetism. The main result of the paper states that the standard V-cycle multigrid technique is both an efficient solver and preconditioner provided that appropriate finite dimensional subspaces of H(div) and H(curl) are chosen and suitable additive or multiplicative Schwarz smoothers are used. The analysis relies on discrete Helmholtz decompositions into subspaces of irrotational and solenoidal vector fields.
[R.H.W.Hoppe (München)]

MSC 2000:: *65N55 Multigrid methods; domain decomposition (BVP of PDE)
35J05 Laplace equation, etc.
65N30 Finite numerical methods (BVP of PDE)

Keywords: multigrid methods; preconditioning; Helmholtz decomposition

Cited in: Zbl 1071.65170

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