doi:10.4208/jcm.1003-m0012 EQUIVALENCE OF SEMI-LAGRANGIAN AND LAGRANGE–GALERKIN SCHEMES UNDER CONSTANT ADVECTION SPEED*

We compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange–Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hy-poteses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equiv-alence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case