Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4645770 | Applied Numerical Mathematics | 2010 | 4 Pages |
The Powell–Sabin (PS) piecewise quadratic C1 finite element on the PS 12-split of a triangulation is a common choice for the construction of a BPX-type preconditioner for the biharmonic equation. In this note we investigate the related Powell–Sabin element on the PS 6-split instead of the PS 12-split for the construction of such preconditioners. For the PS 6-split element multilevel spaces can be created using a -refinement scheme instead of the traditional dyadic scheme. Topologically -refinement has many advantages: it is a slower refinement than the dyadic split operation, and it alternates the orientation of the refined triangles. Therefore we expect a reduction of the amount of work when compared to the PS 12-split element BPX preconditioner, although both methods have the same asymptotical complexity. Numerical experiments confirm this statement.