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

hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorBARON, V.
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOUDIÈRE, Y.
hal.structure.identifierBureau de Recherches Géologiques et Minières [BRGM]
dc.contributor.authorSOCHALA, Pierre
dc.date.accessioned2024-04-04T02:41:05Z
dc.date.available2024-04-04T02:41:05Z
dc.date.issued2017-02
dc.identifier.issn0168-9274
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191121
dc.description.abstractEnWe derive some a posteriori error estimates for the Richards equation. This parabolic equation is nonlinear in space and in time, thus its resolution requires fixed-point iterations within each time step. We measure the approximation error with the dual norm of the residual. A computable upper bound of this error consists of several estimators involving adequate reconstructions based on the degrees of freedom of the scheme. The space and time reconstructions are specified for a two-step backward differentiation formula and a discrete duality finite volume scheme. Our strategy to decrease the computational cost relies on an aggregation of the estimators in three components: space discretization, time discretization, and linearization. We propose an algorithm to stop the fixed-point iterations after the linearization error becomes negligible, and to choose the time step in order to balance the time and space errors. We analyze the influence of the parameters of this algorithm on three test cases and quantify the gain obtained in comparison with a classical simulation.
dc.language.isoen
dc.publisherElsevier
dc.subject.enA posteriori error estimates
dc.subject.enRichards equation
dc.subject.enDiscrete duality finite volume scheme
dc.subject.enBackward differentiation formula
dc.subject.enAdaptive algorithm
dc.title.enAdaptive multistep time discretization and linearization based on a posteriori error estimates for the Richards equation
dc.typeArticle de revue
dc.identifier.doi10.1016/j.apnum.2016.10.005
dc.subject.halPlanète et Univers [physics]/Sciences de la Terre
bordeaux.journalApplied Numerical Mathematics
bordeaux.page104-125
bordeaux.volume112
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03702088
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03702088v1
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