Error estimate for the upwind scheme for the linear transport equation with boundary data

Nina Aguillon (1) , Franck Boyer (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the upwind finite volume scheme on a general mesh for the initial and boundary-value problem associated with a linear transport equation. For any BV initial and boundary data we prove the (optimal) convergence rate 1/2 in the L 1-norm. Compared to previous works, our main contribution is to take into account the boundary data and to relax some regularity assumptions on the velocity field. As an intermediate result, we also provide a complete proof of the BV regularity of weak solutions of such a general transport problem.

Mots clés: BV estimate; transport equation; error estimate; upwind finite volume

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Nina Aguillon, Franck Boyer. Error estimate for the upwind scheme for the linear transport equation with boundary data. IMA Journal of Numerical Analysis, 2018, 38 (2), pp.669-719. ⟨hal-01328667v2⟩