Singular perturbation with a reduced approximation order in space for the transport equation

Mohammed Belhout (1) , Jérôme Pousin (1) , Yves Renard (1)

1 ICJ - Institut Camille Jordan

This work is devoted to singular transport phenomena by convection with fast-low time scales, or to transport in porous media with vanishing discontinuous porosities. For P1-P0 Finite element, by using a reduction of the approximation order for the time differential operator, we propose a numerical method which does not have any oscillations in the neighborhood of the coefficient discontinuity. Error estimates of order one with respect to space are provided. Euler explicit and implicit time schemes are proposed, and by considering a toy problem, the order one of convergence with respect to time and space is checked.

Mots clés: error estimates; singular mass matrix; degenerate operator

Domaines: Analyse numérique [math.NA]

Mohammed Belhout, Jérôme Pousin, Yves Renard. Singular perturbation with a reduced approximation order in space for the transport equation. International Mathematical Forum, 2012, 7 (27), pp.1309-1315. ⟨hal-00761595⟩