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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

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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
  • Corresponding author
  • University of Manouba, ENSI, Campus Universitaire de Manouba, 2010 Manouba, Tunisia; and University of Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 Tunis, Tunisia
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Christine Bernardi
  • Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
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  • Other articles by this author:
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/ Moncef Touihri / Driss Yakoubi
Published Online: 2017-05-11 | DOI: https://doi.org/10.1515/apam-2016-0084


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.

Keywords: Saturated/unsaturated; porous media; spectral methods; space and time discretization; a priori analysis

MSC 2010: 76D05; 76S05


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About the article

Received: 2016-08-15

Revised: 2017-03-26

Accepted: 2017-03-29

Published Online: 2017-05-11

Published in Print: 2018-01-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 9, Issue 1, Pages 1–27, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2016-0084.

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