Ghost solutions with centered schemes for one-dimensional transport equations with Neumann boundary conditions
Mélanie Inglard, Fré́dé́ric Lagoutière, Hans Henrik Rugh · Annales de la faculté des sciences de Toulouse Mathématiques · 2020
This paper is devoted to the space-centered θ -scheme for the transport equation with constant velocity on an interval, with homogeneous Neumann boundary data on each side. The numerical solution presents a weird behavior, as if the initial datum was periodical over ℝ , with a period that would be twice or four times (depending on the case) the length of the considered interval. We precisely formulate this statement and prove it. We also study a similar behavior in the case of Dirichlet boundary conditions.