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Finite element wavelets on manifolds

By H. Nguyen and R. Stevenson


We construct locally supported, continuous wavelets on manifolds G that\ud are given as the closure of a disjoint union of general smooth parametric images of an\ud n-simplex. The wavelets are proven to generate Riesz bases for Sobolev spaces Hs(G)\ud when s E (-1, 3/2 ), if not limited by the global smoothness of G. These results generalize\ud the findings from [DSt99], where it was assumed that each parametrization has a constant\ud Jacobian determinant. The wavelets can be arranged to satisfy the cancellation property of\ud in principal any order, except for wavelets with supports that extend to different patches,\ud which generally satisfy the cancellation property of only order 1

Topics: Wiskunde en Informatica, finite elements, wavelets, Riesz bases, vanishing moments, boundary integral equations
Year: 2001
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