A two-grid hybrid finite element method for the single-phase crustal stress coupling problems in porous media
In this paper,a two-grid hybrid finite element method is proposed for the coupled crustal stress problems of single-phase flow in porous media.First,the governing equation for the single-phase flow in po-rous media and the crustal stress problem are given,the nonlinear governing equation for the single-phase flow coupling the crustal stress problem of micro compressible fluid in porous media is derived.Second,the two-grid hybrid element method is given for solving the nonlinear governing equation by transforming the problem of solving nonlinear governing equation into solving some small-scale nonlinear problems on coarse grids as well as solving some large-scale linear problems on fine grids.A mixed finite element is used to dis-crete the single-phase flow coupled crustal stress model,corresponding numerical algorithm is designed and appropriate parameters are selected.Due to the fact that the subdivision on the coarse grid can be very rough,it can be considered that the time required to compute the nonlinear equations on the coarse grid is negligible,thereby significantly improving the computational efficiency.Finally,numerical examples verify the perfor-mance of the method.
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