A Posteriori Error Analysis of the Method of Characteristics

Christine Bernardi (1) , Frédéric Hecht (1) , Rüdiger Verfürth (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Fakultät für Mathematik

We consider a two- or three-dimensional timedependent diusion-convection-reaction problem and its discretization by the method of characteristics and standard nite elements. We perform the a posteriori error analysis of this discretization and prove optimal error estimates, which lead to an ecient adaptivity strategy both for the time step and the spatial mesh. The estimates are robust with respect to the ratios of the diusion to the reaction or convection. Some numerical experiments support the theoretical results.

Domaines: Analyse numérique [cs.NA]

Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth. A Posteriori Error Analysis of the Method of Characteristics. Mathematical Models and Methods in Applied Sciences, 2009, 21 (06), pp.1355-1377. ⟨10.1142/S0218202511005337⟩. ⟨hal-00395280⟩