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Multigrid methods with Powell-Sabin splines. (English) Zbl 1158.65084
The authors present a multigrid method for elliptic boundary-value problems on polygonal domains in the plane. The basis functions are Powell-Sabin splines implemented as in their earlier paper [J. Comput. Appl. Math. 189, 643–659 (2006; Zbl 1086.65114)]. These splines are $$C^1$$ cubics. It is shown that the number of iterations required to attain a specific accuracy is bounded independent of the mesh size.

##### MSC:
 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations
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