Two-grid mixed finite element method for nonlinear multi-physical quantities problem of the single-phase flow coupled with geostress in porous media

Abstract

A numerical method for the strongly nonlinear model of the single-phase flow coupled with the geostress in the geologic reservoir with multi-physical features such as shale gas pressure, velocity, geostress, porosity, and structural displacement is studied in this paper. A two-grid Crank-Nicolson mixed finite element (CNMFE) method is developed for the nonlinear model and the unconditional stability and convergence as well as errors for the CNMFE solutions are analyzed. The correctness of theoretical results is validated by numerical experiments. We hope our work will facilitate the theoretical study of porous media problems.