The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows (Communications in Computational Physics, 2020)
The paper is concerned with the unconditional stability and error estimatesof fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscibleflows in porous media. We prove that the optimal L2 error estimates hold without anytime-step (convergence) conditions, while all previous works require certain time-steprestrictions. Theoretical analysis is based on a splitting of the error into two parts: theerror from the time discretization of the PDEs and the error from the finite elementdiscretization of the corresponding time-discrete PDEs, which was proposed in ourprevious work [26, 27]. Numerical results for both two- and three-dimensional flowmodels are presented to confirm our theoretical analysis.