Regular Article
Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect
1
Energy Research Laboratory, College of Engineering, Effat University, 21478 Jeddah, Kingdom of Saudi Arabia
2
Department of Mathematics, Faculty of Science, Aswan University, 81528 Aswan, Egypt
3
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000 Hubei, PR China
4
Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900 Jeddah, Kingdom of Saudi Arabia
* Corresponding author: momousa@effatuniversity.edu.sa
Received:
6
February
2020
Accepted:
6
April
2020
In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.
© M.F. El-Amin et al., published by IFP Energies nouvelles, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.