Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients

Laurent Gosse (1) , Francois James (2)

1 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equations admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-differences numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.

Mots clés: Linear conservation equations; duality solutions; finite difference schemes; weak consistency; nonconservative product

Domaines: Analyse numérique [math.NA]

Laurent Gosse, Francois James. Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients. Mathematics of Computation, 2000, 69 (231), pp.987 - 1015. ⟨10.1090/S0025-5718-00-01185-6⟩. ⟨hal-00419729⟩