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Uniformly stable wavelets on nonuniform triangulations

Author

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  • Bruvoll, Solveig
  • Lyche, Tom
  • Mørken, Knut

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.

Suggested Citation

  • Bruvoll, Solveig & Lyche, Tom & Mørken, Knut, 2017. "Uniformly stable wavelets on nonuniform triangulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 177-200.
  • Handle: RePEc:eee:matcom:v:137:y:2017:i:c:p:177-200
    DOI: 10.1016/j.matcom.2016.09.006
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