Finite element wavelets with improved quantitative properties

• 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 H-s for |s| less than 3/2 (or |s| less than= 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.

Nyckelord

Finite element; Wavelet; Riesz basis; Cancellation property; Partial differential equation; Boundary integral equation

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