Skip to Main content Skip to Navigation
Directions of work or proceedings

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

Vincent Baron 1, 2 Yves Coudière 3, 4 Pierre Sochala 1
1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IHU-LIRYC, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
4 IMB - Institut de Mathématiques de Bordeaux
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.
keyword : A posteriori estimate Richards equation Discrete Duality Finite Volume scheme adaptive algorithm
Document type :
Directions of work or proceedings
Complete list of metadata
https://hal.inria.fr/hal-00983512
Contributor : Vincent Baron <>
Submitted on : Friday, April 25, 2014 - 2:04:47 PM
Last modification on : Saturday, May 18, 2019 - 9:38:03 PM

Identifiers

  • HAL Id : hal-00983512, version 1

Collections

BRGM | CNRS | INRIA | IMB | FMPL | LMJL | INSMI | UNIV-NANTES | CHL | DRP | TDS-MACS

Citation

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⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

595

 

Contact                    Legal Notice                    Personal Data