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