The course will cover several topics in discretizations of partial differential equations and the solution of the resulting algebraic systems. Topics in discretizations will include mixed finite element methods, finite volume methods, mimetic finite difference methods, and local discontinuous Galerkin methods. Topics in solvers will include domain decomposition methods and multigrid methods. Applications to flow and transport in porous media, as well as coupled fluid and porous media flows will be discussed. The computational exercises will involve running codes on the departmental shared and distributed memory parallel computers.
Written homework and computational projects will be assigned. A programming language of choice can be used. Help will only be provided for Matlab and Fortran. The finite element package Freefem++ will be used for some of the computer assignments.