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Quadratic Spline Wavelets with Short Support for Fourth-Order Problems

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Abstract

In the paper, we propose constructions of new quadratic spline-wavelet bases on the interval and the unit square satisfying homogeneous Dirichlet boundary conditions of the second order. The basis functions have small supports and wavelets have one vanishing moment. We show that stiffness matrices arising from discretization of the biharmonic problem using a constructed wavelet basis have uniformly bounded condition numbers and these condition numbers are very small.

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Authors and Affiliations

  1. Department of Mathematics and Didactics of Mathematics, Technical University of Liberec, Studentská 2, 461 17, Liberec, Czech Republic

    Dana Černá & Václav Finěk

Authors
  1. Dana Černá
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  2. Václav Finěk
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Correspondence to Dana Černá.

Additional information

The authors have been supported by the ESF project “Strengthening international cooperation of the KLIMATEXT research team” No. CZ.1.07/2.3.00/20.0086.

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Černá, D., Finěk, V. Quadratic Spline Wavelets with Short Support for Fourth-Order Problems. Results. Math. 66, 525–540 (2014). https://doi.org/10.1007/s00025-014-0402-6

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  • DOI: https://doi.org/10.1007/s00025-014-0402-6

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