TY - JOUR
T1 - A Technique for High-Order Treatment of Diffusion Terms in Semi-Lagrangian Schemes
AU - Roberto Ferretti
JO - Communications in Computational Physics
VL - 2
SP - 445
EP - 470
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.070709.011209a
UR - https://global-sci.org/intro/article_detail/cicp/7580.html
KW - 
AB - <p style="text-align: justify;">We consider in this paper a high-order, semi-Lagrangian technique to treat
possibly degenerate advection-diffusion equations, which has been proposed in similar
forms by various authors. The scheme is based on a stochastic representation
formula for the solution, which allows to avoid the splitting between advective and
diffusive part of the evolution operator. A general theoretical analysis is carried out in
the paper, with a special emphasis on the possibility of using large Courant numbers,
and numerical tests in one and two space dimensions are presented.</p>