Non linear finite volume schemes for the heat equation in 1D.

Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We construct various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier's trick [CRAS Paris, I 348, 2010]. They preserve the maximum principle and admit a finite volume formulation. We provide a functional setting for the analysis of convergence of such methods. Finally we construct, analyze and test a new explicit non linear maximum preserving scheme: we prove third order convergence: it is optimal on numerical tests.

Domaines: Analyse numérique [cs.NA]

Bruno Després. Non linear finite volume schemes for the heat equation in 1D.. 2012. ⟨hal-00714781⟩