Mixed finite element approximation for a coupled petroleum reservoir model
Amara, Mohamed ; Capatina-Papaghiuc, Daniela ; Denel, Bertrand ; Terpolilli, Peppino
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005), p. 349-376 / Harvested from Numdam
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In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature. The discrete problem thus obtained is well-posed and a posteriori error estimates are also established. Numerical tests are presented validating the developed code.

Publié le : 2005-01-01
DOI : https://doi.org/10.1051/m2an:2005015
Classification:  35Q35,  65N15,  65N30,  76S05 
@article{M2AN_2005__39_2_349_0,
     author = {Amara, Mohamed and Capatina-Papaghiuc, Daniela and Denel, Bertrand and Terpolilli, Peppino},
     title = {Mixed finite element approximation for a coupled petroleum reservoir model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {39},
     year = {2005},
     pages = {349-376},
     doi = {10.1051/m2an:2005015},
     mrnumber = {2143952},
     zbl = {1130.76045},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2005__39_2_349_0}
}

Amara, Mohamed; Capatina-Papaghiuc, Daniela; Denel, Bertrand; Terpolilli, Peppino. Mixed finite element approximation for a coupled petroleum reservoir model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 349-376. doi : 10.1051/m2an:2005015. http://gdmltest.u-ga.fr/item/M2AN_2005__39_2_349_0/

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