Analysis of Direct Three-Dimensional Parabolic Panel Methods

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.