Finite element wavelets with improved quantitative properties

H. Nguyen; R.P. Stevenson

doi:10.1016/j.cam.2009.01.007

Finite element wavelets with improved quantitative properties

H. Nguyen, R.P. Stevenson

Dept of Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319 352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for jsj <32 (or jsj 1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.

Original language	English
Pages (from-to)	706-727
Number of pages	22
Journal	Journal of Computational and Applied Mathematics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2009.01.007
Publication status	Published - 2009

Keywords

Wiskunde en Informatica (WIIN)
Mathematics
Wiskunde en computerwetenschappen
Landbouwwetenschappen
Wiskunde: algemeen

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T1 - Finite element wavelets with improved quantitative properties

AU - Nguyen, H.

AU - Stevenson, R.P.

PY - 2009

Y1 - 2009

N2 - In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319 352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for jsj <32 (or jsj 1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.

AB - In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319 352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for jsj <32 (or jsj 1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.

KW - Wiskunde en Informatica (WIIN)

KW - Mathematics

KW - Wiskunde en computerwetenschappen

KW - Landbouwwetenschappen

KW - Wiskunde: algemeen

U2 - 10.1016/j.cam.2009.01.007

DO - 10.1016/j.cam.2009.01.007

M3 - Article

SN - 0377-0427

VL - 230

SP - 706

EP - 727

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Finite element wavelets with improved quantitative properties

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