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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2017

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

Résumé

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.
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Dates et versions

hal-01342386 , version 1 (05-07-2016)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Konstantin Brenner, Clément Cancès. Improving Newton's method performance by parametrization: the case of Richards equation. SIAM Journal on Numerical Analysis, 2017, 55 (4), pp.1760--1785. ⟨hal-01342386⟩
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