Uniformly stable wavelets on nonuniform triangulations

Solveig Bruvoll, Tom Lyche and Knut Mørken

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 137, issue C, 177-200

Abstract: In this paper we construct linear, uniformly stable, wavelet-like functions on arbitrary triangulations. As opposed to standard wavelets, only local orthogonality is required for the wavelet-like functions. Nested triangulations are obtained through refinement by two standard strategies, in which no regularity is required. One strategy inserts a new node at an arbitrary position inside a triangle and then splits the triangle into three smaller triangles. The other strategy splits two neighbouring triangles into four smaller triangles by inserting a new node somewhere on the edge between the triangles. In other words, non-uniform refinement is allowed in both strategies. The refinement results in nested spaces of piecewise linear functions. The detail-, or wavelet-spaces, are made to satisfy certain orthogonality conditions which locally correspond to vanishing linear moments. It turns out that this construction is uniformly stable in the L∞ norm, independently of the geometry of the original triangulation and the refinements.

Keywords: Wavelets; Approximation; Stability; Non-uniform triangulations (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:137:y:2017:i:c:p:177-200

DOI: 10.1016/j.matcom.2016.09.006

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