This paper presents a multigrid algorithm for the solution of the linear systems that arise from a finite-element discretization of second-order elliptic partial differential equations with Powell-Sabin (PS) splines. We show that the method yields a uniform convergence in the l2-norm which is independent of the mesh size. We also briefly consider the use of PS splines for the fourth-order biharmonic problem.
Speleers, H., Dierckx, P., Vandewalle, S. (2008). Multigrid methods with Powell-Sabin splines. IMA JOURNAL OF NUMERICAL ANALYSIS, 28(4), 888-908 [10.1093/imanum/drm031].
Multigrid methods with Powell-Sabin splines
Speleers H.;
2008-10-01
Abstract
This paper presents a multigrid algorithm for the solution of the linear systems that arise from a finite-element discretization of second-order elliptic partial differential equations with Powell-Sabin (PS) splines. We show that the method yields a uniform convergence in the l2-norm which is independent of the mesh size. We also briefly consider the use of PS splines for the fourth-order biharmonic problem.File in questo prodotto:
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