Stabilizing the Hierarchical Basis by Approximate Wavelets
نویسندگان
چکیده
This paper proposes a stabilization of the classical hierarchical basis (HB)-nite element method by modifying the standard nodal basis functions that correspond to the hierarchical complement (in the next ner discretization space) of any successive coarse dis-cretization space using computationally feasible approximate L 2 {projections onto the given coarse space. The corresponding multilevel additive and product algorithms give spectrally equivalent preconditioners and one action of such a preconditioner is of almost optimal order. The major results are regularity{free for the continuous problem (second order elliptic) and can be applied to problems with local reenement. Numerical results that illustrate the theory are presented.
منابع مشابه
Stabilizing the Hierarchical Basis by Approximate Wavelets II: Implementation and Numerical Results
This paper is the second part of a work on stabilizing the classical hierarchical basis HB by using wavelet-like basis functions. Implementation techniques are of major concern for the multilevel preconditioners proposed by the authors in the first part of the work, which deals with algorithms and their mathematical theory. Numerical results are presented to confirm the theory established there...
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