Analysis of Direct Three-Dimensional Parabolic Panel Methods

Philippe Poncet (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

Adherence boundary conditions for time dependent partial differential equations, via Chorin algorithm, can be reduced to a parabolic problem with Robin-Fourier boundary conditions in the three-dimensional context. In the spirit of panel methods, one establishes an integral formulation whose key point is the estimation of the potential density, introducing a kind of panel method for tangential kinematic boundary conditions. This paper discusses explicit estimations of this density in the general case of an arbitrarily shaped three-dimensional body, which leads to a fast numerical scheme. An error analysis is also provided, involving body smoothness, the Hölder exponent of the density, and whether the body presents torsion or not.

Mots clés: parabolic equations; fundamental solutions; integral representation; boundary value problems; growth of solutions; numerical analysis

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]; Géométrie métrique [math.MG]

Philippe Poncet. Analysis of Direct Three-Dimensional Parabolic Panel Methods. SIAM Journal on Numerical Analysis, 2007, 45 (6), pp.2259-2297. ⟨10.1137/050625849⟩. ⟨hal-02010650⟩