Convergence Analysis of Backward Semi-Lagrangian Scheme with Bdf2 in Non-Linear Advection-Diffusion Problems
In this paper, we give a convergence analysis of a backward semi-Lagrangian scheme in a finite difference
method for Burgers' equation. We apply an iteration free error correction method to solve characteristic curves of particles.
We also adopt BDF2 and second order central difference method in time and space, respectively, for the time dependent
diffusion equation along the characteristic curves.In the sense of the discrete ℓ-norm, we show that the proposed scheme
has the convergencebehavior O(h + Δx + Δ
, where h, Δx, and are the time, spatial grid size, and the order of
interpolations, respectively.A numerical test is provided to support the validity of the theoretical estimates.
Index Terms—Burgers' equation, Error Analysis, Semi-Lagrangian Scheme, Error Correction Method, non-linear advectiondiffusion