A finite volume scheme for noncoercive elliptic equation with measure data

Jerome Droniou (1) , Thierry Gallouët (2) , Raphaele Herbin (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We show here the convergence of the finite volume approximate solutions of a convection-diffusion equation to a weak solution, without the usual coercitivity assumption on the elliptic operator and with weak regularity assumptions on the data. Numerical experiments are performed to obtain some rates of convergence in two and three space dimensions.

Mots clés: elliptic equations; noncoercive; measure data; finite volume

Domaines: Analyse numérique [math.NA]

Jerome Droniou, Thierry Gallouët, Raphaele Herbin. A finite volume scheme for noncoercive elliptic equation with measure data. SIAM Journal on Numerical Analysis, 2003, 41 (6), pp.1997-2031. ⟨10.1137/S0036142902405205⟩. ⟨hal-00003440⟩