Uniformly stable wavelets on nonuniform triangulations

Author
Bruvoll, Solveig
Lyche, Tom Johan
Mørken, Knut Martin
Date Issued
2016
Keywords
Triangulering
Permalink
http://hdl.handle.net/20.500.12242/607
https://publications.ffi.no/123456789/607
DOI
10.1016/j.matcom.2016.09.006
Collection
Articles
Description
Bruvoll, Solveig; Lyche, Tom Johan; Mørken, Knut Martin. Uniformly stable wavelets on nonuniform triangulations. Mathematics and Computers in Simulation 2016
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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.
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