Abstract:
We develop several a-priori and a-posteriori error estimates for two-grid finite element discretization of coupled elliptic and parabolic systems with a set of parameters P. We present numerical results that verify the convergence order of the numerical schemes predicted by the a-priori estimates. We present numerical results that verify the robustness of the estimators developed with respect to the two-grid discretization and with respect to the parameters P. The theoretical and numerical results in this thesis apply to models of many important phenomena in fluid flow and transport in porous media. We demonstrate some applications with numerical simulations.
