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A priori error analysis of the implicit Euler, spectral discretization of a nonlinear equation for a flow in a partially saturated porous media

  • Nahla Abdellatif EMAIL logo , Christine Bernardi , Moncef Touihri and Driss Yakoubi

Abstract

The aim of this work is the numerical study of a nonlinear equation, which models the water flow in a partially saturated underground porous medium under the surface. We propose a discretization of this equation that combines Euler’s implicit scheme in time and spectral methods in space. We prove optimal error estimates between the continuous and discrete solutions. Some numerical experiments confirm the interest of this approach. We present numerical experiments which are in perfect coherence with the analysis.

MSC 2010: 76D05; 76S05

Acknowledgements

We are deeply grateful to Linda El Alaoui who revealed us the existence of this equation due to Richards and showed her high interest for our work.

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Received: 2016-8-15
Revised: 2017-3-26
Accepted: 2017-3-29
Published Online: 2017-5-11
Published in Print: 2018-1-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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