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

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.
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https://hal.inria.fr/hal-00983512
Contributor : Vincent Baron Connect in order to contact the contributor
Submitted on : Friday, April 25, 2014 - 2:04:47 PM
Last modification on : Sunday, June 26, 2022 - 10:10:15 AM

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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, ⟨10.1007/978-3-319-05591-6_48⟩. ⟨hal-00983512⟩

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