TY - JOUR
T1 - Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed
AU - Roberto Ferretti
JO - Journal of Computational Mathematics
VL - 4
SP - 461
EP - 473
PY - 2010
DA - 2010/08
SN - 28
DO - http://doi.org/10.4208/jcm.1003-m0012
UR - https://global-sci.org/intro/article_detail/jcm/8532.html
KW - Semi-Lagrangian schemes, Lagrange-Galerkin schemes, Stability.
AB - <p style="text-align: justify;">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 hypotheses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case.</p>