TY - JOUR
T1 - The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows
JO - Communications in Computational Physics
VL - 4
SP - 1141
EP - 1158
PY - 2014
DA - 2014/04
SN - 15
DO - http://doi.org/10.4208/cicp.080313.051213s
UR - https://global-sci.org/intro/article_detail/cicp/7131.html
KW - 
AB - <p style="text-align: justify;">The paper is concerned with the unconditional stability and error estimates
of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible
flows in porous media. We prove that the optimal L<sup>2&nbsp;</sup>error estimates hold without any
time-step (convergence) conditions, while all previous works require certain time-step
restrictions. Theoretical analysis is based on a splitting of the error into two parts: the
error from the time discretization of the PDEs and the error from the finite element
discretization of the corresponding time-discrete PDEs, which was proposed in our
previous work [26, 27]. Numerical results for both two- and three-dimensional flow
models are presented to confirm our theoretical analysis.</p>