Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect
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: firstname.lastname@example.org
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
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