讲座内容：

In this talk，we study the fully discrete finite element methods for the porous media flow with weak regularity coefficient. Previous works on optimal-order L^{\infty}(L^2)-norm error estimate required the strong regularity assumption, while the Bear–Scheidegger diffusion–dispersion tensor is only Lipschitz continuous even for a sufficiently smooth velocity field u. In this work, by maximal L^p-regularity of fully discrete finite element solutions of parabolic  equation, optimal error estimate in L^p (L^q) -norm and almost optimal error estimate in L{\infty} (L^q )-norm are established under the assumption of coefficient being Lipschitz continuous.