Abstract : We derive some a posteriori error estimates for the Richards equation, based on the dual norm of the residual. This equation is nonlinear in space and in time, thus its resolution requires fixed-point iterations within each time step. We propose a strategy to decrease the computational cost relying on a splitting of the error terms in three parts: linearization, time discretization, and space discretization. In practice, we stop the fixed-point iterations after the linearization error becomes negligible, and choose the time step in order to balance the time and space errors.
https://hal.inria.fr/hal-00983512
Contributeur : Vincent Baron
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Soumis le : vendredi 25 avril 2014 - 14:04:47
Dernière modification le : jeudi 5 avril 2018 - 10:36:09
Vincent Baron, Yves Coudière, Pierre Sochala. Adaptive time discretization and linearization based on a posteriori estimates for the Richards equation. Fuhrmann, Jürgen; Ohlberger, Mario; Rohde, Christian. France. Springer, 8 p., 2014, Springer Proceedings in Mathematics & Statistics, Vol. 77. 〈hal-00983512〉
