A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes (Communications in Computational Physics, 2010)
We consider in this paper a high-order, semi-Lagrangian technique to treatpossibly degenerate advection-diffusion equations, which has been proposed in similarforms by various authors. The scheme is based on a stochastic representationformula for the solution, which allows to avoid the splitting between advective anddiffusive part of the evolution operator. A general theoretical analysis is carried out inthe paper, with a special emphasis on the possibility of using large Courant numbers,and numerical tests in one and two space dimensions are presented.