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Discontinuous Galerkin Methods pp 301–308Cite as

Introduction to Discontinuous Wavelets

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 11))

Abstract

Wavelets provide a tool for efficient representation of functions. This efficient representation has proven useful in the numerical solution of non-linear evolution equations. In this paper we provide a brief review of the use of wavelets for efficient representation of functions, and in particular we describe the piecewise-discontinuous basis of wavelets proposed by Alpert. We review the useful properties this basis has for the solution of PDE’s, and introduce an illustrative approach to the representation of boundary conditions. We also discuss the extension to higher dimensional problems.

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References

  1. B. Alpert. A Class of Bases in l 2 for the Sparse Representation of Integral Operators. SIAM J. Math. Anal, 24 (1): 246–262, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi. Adaptive solution of partial differential equations in multiwavelet bases. Preprint, 1999.

    Google Scholar 

  3. G. Beylkin, R. R. Coifman, and V. Rokhlin. Fast wavelet transforms and numerical algorithms I. Comm. Pure and Appl. Math., 44:141–183, 1991. Yale University Technical Report YALEU/DCS/RR-696, August 1989.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Beylkin and J. M. Keiser. On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases. J. Comput. Phys., 132 (2): 233–259, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  5. I. Daubechies. Ten Lectures on Wavelets. CBMS-NSF Series in Applied Mathematics. SIAM, 1992.

    MATH  Google Scholar 

  6. Spencer J. Sherwin and George Em. Karniadakis. A new triangular and tetrahedral basis for high-order (hp) finite element methods. Internat. J. Numer. Methods Engrg., 38 (22): 3775–3802, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. von Petersdorff, C. Schwab, and R. Schneider. Multiwavelets for second-kind integral equations. SIAM J. Numer. Anal., 34 (6): 2212–2227, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Yu, K. Kolarov, and W. Lynch. Barysymmetric multiwavelets on triangle. Preprint, March 1997.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 55455, USA

    Nicholas Coult

Authors
  1. Nicholas Coult
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George E. Karniadakis  & Chi-Wang Shu  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Coult, N. (2000). Introduction to Discontinuous Wavelets. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_25

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64098-8

  • Online ISBN: 978-3-642-59721-3

  • eBook Packages: Springer Book Archive

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