Adaptive multistep time discretization and linearization based on a posteriori estimates for the Richards equation

Pierre Sochala (1) , Vincent Baron (2) , Yves Coudière (3, 4)

1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)
2 UN - Université de Nantes
3 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
4 IMB - Institut de Mathématiques de Bordeaux

We derive a posteriori error estimates based on the dual norm of the residual of the Richards equation. The error is decomposed into space, time, and linearization terms. Error estimators are computed with reconstructions especially designed for a multistep Discrete Duality Finite Volume scheme. We stop the fixed-point iterations when the linearization error becomes negligible, and we choose the time step to balance the time and space errors. Results are presented to several test cases.

Mots clés: discrete duality finite volume reconstructions; Computable error estimators; error balancing

Domaines: Modélisation et simulation

Pierre Sochala, Vincent Baron, Yves Coudière. Adaptive multistep time discretization and linearization based on a posteriori estimates for the Richards equation. SIAM Conference on Mathematical and Computational Issues in the Geosciences, SIAM, Jun 2015, Stanford, United States. ⟨hal-01148742⟩