Divergence-free and Curl-free Wavelets on the Square for Numerical Simulations

  title={Divergence-free and Curl-free Wavelets on the Square for Numerical Simulations},
  author={Val{\'e}rie Perrier},
We present a construction of divergence-free and curl-free wavelets on the square, that could satisfy suitable boundary conditions. This construction is based on the existence of biorthogonal multiresolution analyses (BMRA) on [0, 1], linked by differentiation and integration. We introduce new BMRAs and wavelets for the spaces of divergence-free and curl-free vector functions on the square. The interest of such constructions is illustrated on examples including the Helmholtz-Hodge decomposition… CONTINUE READING
2 Citations
26 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 26 references

Analyse multirésolution biorthogonale sur l’intervalle et applications

  • A. Jouini, P. G. Lemarié-Rieusset
  • Annales de l’I.H.P. Section C 10
  • 1993
Highly Influential
17 Excerpts

Raviart, Finite element methods for Navier-Stokes equations Springer-Verlag Berlin

  • P.A.V. Girault
  • 1986
Highly Influential
20 Excerpts

Numerical Analysis of Wavelet Methods

  • A. Cohen
  • 2003
Highly Influential
4 Excerpts

Wavelet on the interval with optimal localization

  • S. Grivet-Talocia, A. Tabacco
  • Math. Models. Meth. Appl. Sci. 10(3)
  • 2000
Highly Influential
8 Excerpts

Analyses multi-résolutions non orthogonales

  • P. G. Lemarié-Rieusset
  • commutation entre projecteurs et dérivation et…
  • 1992
Highly Influential
7 Excerpts

Orthogonal Wavelet Bases Adapted For Partial Differential Equations With Boundary Conditions

  • P. Monasse, V. Perrier
  • SIAM J.Math. Anal. 29
  • 1998
Highly Influential
10 Excerpts


  • A. Cohen
  • Daubechies, J.-C. Feauveau, Biorthogonal bases of…
  • 1992
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…