Titre :

Improving Newton's method performance by parametrization: the case of Richards equation

Auteur(s) :

Brenner, Konstantin [Auteur]
COmplex Flows For Energy and Environment [COFFEE]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

SIAM Journal on Numerical Analysis

Pagination :

1760--1785

Éditeur :

Society for Industrial and Applied Mathematics

Date de publication :

2017

ISSN :

0036-1429

Mot(s)-clé(s) en anglais :

Finite Volumes
parametrization
Newton's method
Richards equation

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Planète et Univers [physics]/Sciences de la Terre/Hydrologie

Résumé en anglais : [en]

The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new ...
Lire la suite >The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for the continuous equation in order to stabilize Newton's method by parametrizing the graph linking the pressure and the saturation. The resulting form of Richards equation is then discretized thanks to a monotone Finite Volume scheme. We prove the well-posedness of the numerical scheme. Then we show under appropriate non-degeneracy conditions on the parametrization that Newton’s method converges locally and quadratically. Finally, we provide numerical evidences of the efficiency of our approach.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL