Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes

Christophe Buet (1) , Bruno Després (2) , Emmanuel Franck (3) , Thomas Leroy (1, 2)

1 DSSI - Département des Sciences de la Simulation et de l'Information
2 LJLL - Laboratoire Jacques-Louis Lions
3 IPP - Max-Planck-Institut für Plasmaphysik [Garching]

We prove the uniform AP convergence on unstructured meshes in 2D of a generalization, of the Gosse-Toscani 1D scheme for the hyperbolic heat equation. This scheme is also a nodal extension in 2D of the Jin-Levermore scheme described in [18] for the 1D case. In 2D, the proof is performed using a new diffusion scheme.

Mots clés: asymptotic preserving; uniform convergence; nodal scheme; hyperbolic heat equation; finite volume; unstructured meshes

Domaines: Analyse numérique [math.NA]

Christophe Buet, Bruno Després, Emmanuel Franck, Thomas Leroy. Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes. 2014. ⟨hal-00956573v2⟩