Semi-Lagrangian methods for diffusion problems

I will review some recent joint work with R. Ferretti (Roma3) on semi-Lagrangian methods for parabolic problems in divergence form. Both non conservative and flux form, conservative approaches will be presentedand analyzed, showing how large time steps can be used without loss of accuracy for both linear and nonlinear problems. Numerical examples validate the proposed methods and display its potential for consistent semi-Lagrangian discretization of advection{ diffusion and nonlinear parabolic problems.