Speleers, Hendrik; Dierckx, Paul; Vandewalle, Stefan Multigrid methods with Powell-Sabin splines. (English) Zbl 1158.65084 IMA J. Numer. Anal. 28, No. 4, 888-908 (2008). 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. Reviewer: Gerald W. Hedstrom (Pleasanton) Cited in 1 Document 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 Keywords:finite-element method; Powell-Sabin splines; multigrid method; elliptic boundary-value problems PDF BibTeX XML Cite \textit{H. Speleers} et al., IMA J. Numer. Anal. 28, No. 4, 888--908 (2008; Zbl 1158.65084) Full Text: DOI