A priori error analysis of an Euler implicit, spectral discretization of Richards equation

Nahla Abdellatif (1, 2) , C Bernardi (3) , M Touihri (4) , D Yakoubi (5)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 ENSI - École Nationale des Sciences de l'Informatique [Manouba]
3 LJLL - Laboratoire Jacques-Louis Lions
4 Ecole de l'aviation de Borj El Amri, Tunisia.
5 The Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario M5T 3J1, Canada.

The aim of this work is the numerical study of Richards 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.

Mots clés: Richards equation; spectral methods; space and time discretization; a priori analysis

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Nahla Abdellatif, C Bernardi, M Touihri, D Yakoubi. A priori error analysis of an Euler implicit, spectral discretization of Richards equation. 2016. ⟨hal-01334559⟩