Two-grid a-priori and a-posteriori Error Analysis for Coupled Elliptic and Parabolic Systems with Applications to Flow and Transport Problems

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.