Divergence-free and curl-free wavelets on the square for numerical simulations

Souleymane Kadri Harouna (1) , Valérie Perrier (2)

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

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.

Mots clés: Divergence-free and curl-free wavelets; Helmholtz-Hodge decomposition; Stokes problem

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Souleymane Kadri Harouna, Valérie Perrier. Divergence-free and curl-free wavelets on the square for numerical simulations. 2011. ⟨hal-00558474v2⟩