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 of vector flows and the Stokes problem.
Publié le : 2011-01-21
Classification:
Divergence-free and curl-free wavelets,
Helmholtz-Hodge decomposition,
Stokes problem,
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00558474,
author = {Kadri Harouna, Souleymane and Perrier, Val\'erie},
title = {Divergence-free and curl-free wavelets on the square for numerical simulations},
journal = {HAL},
volume = {2011},
number = {0},
year = {2011},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00558474}
}
Kadri Harouna, Souleymane; Perrier, Valérie. Divergence-free and curl-free wavelets on the square for numerical simulations. HAL, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/hal-00558474/