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

@inproceedings{Perrier2011DivergencefreeAC,
  title={Divergence-free and Curl-free Wavelets on the Square for Numerical Simulations},
  author={Val{\'e}rie Perrier},
  year={2011}
}
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
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