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Adaptive Time Discretization and Linearization Based on a Posteriori Estimates for the Richards Equation

  • Vincent Baron
  • Yves Coudière
  • Pierre Sochala
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)

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.

Keywords

Space Discretization Posteriori Error Estimate Posteriori Estimate Richards Equation Nonlinear Iteration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.BRGMOrléansFrance
  2. 2.IMBTalence cedexFrance

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