Finite-element wavelets on manifolds |
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Authors: | Nguyen Hoang; Stevenson Rob |
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Institution: |
1 Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
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Abstract: | We construct locally supported, continuous wavelets on manifolds that are given as the closure of a disjoint union of generalsmooth parametric images of an n-simplex. The wavelets are provento generate Riesz bases for Sobolev spaces Hs ( ) when s (1,3/2), if not limited by the global smoothness of . These resultsgeneralize the findings from Dahmen & Stevenson (1999) SIAMJ. Numer. Anal., 37, 319352, where it was assumed thateach parametrization has a constant Jacobian determinant. Thewavelets can be arranged to satisfy the cancellation propertyof, in principle, any order, except for wavelets with supportsthat extend to different patches, which generally satisfy thecancellation property of only order 1. |
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Keywords: | finite elements wavelets Riesz bases vanishing moments boundary integral equations |
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