Powell-Sabin spline based multilevel preconditioners for the biharmonic equation

DOI10.1016/j.apnum.2010.01.002zbMath1190.65175OpenAlexW1988310740MaRDI QIDQ973087

Adhemar Bultheel, Jan Maes

Publication date: 28 May 2010

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.01.002

zbMATH Keywords

multilevelnumerical experimentsfinite elementbiharmonic equationmesh refinementPowell-Sabin splinesBPX preconditioner

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for higher-order elliptic equations (35J40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Preconditioners for iterative methods (65F08)

Cites Work

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• \(C^ 1\)-hierarchical bases
• Automatic construction of control triangles for subdivided Powell --- Sabin splines
• Multilevel finite element preconditioning for √3 refinement
• Hierarchical Conforming Finite Element Methods for the Biharmonic Equation
• Piecewise Quadratic Approximations on Triangles
• Multilevel Algorithms Considered as Iterative Methods on Semidefinite Systems
• Wavelet Least Squares Methods for Boundary Value Problems

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