The course is taught jointly with Prof. Beatrice Riviere
The course will cover several topics in discretizations of partial differential equations. In particular we will study mixed finite element methods, finite volume methods, and discontinuous Galerkin methods. Stability, accuracy, and efficiency of the methods will be discussed. Both steady-state and time-dependent problems will be considered. Applications to single-phase and two-phase flow in porous media, porous media transport, and coupled fluid and porous media flows will be emphasized. The computational exercises will involve running codes on the departmental shared and distributed memory parallel computers.
Written homework and computational projects will be assigned. The finite element package Freefem++ will be used for some of the computer assignments.