Finite element methods

This lecture introduces finite element methods for solving diffusion problems in porous media. It covers topics such as meshing, interpolation, method of weighted residuals, steady-state diffusion equations, boundary conditions, and the implementation of a finite element program. The instructor explains the transformation of continuum problems into a finite number of equations using a mesh, the concept of trial functions and shape functions for interpolation, and the application of weighted residuals to approximate solutions. The lecture also discusses the assembly of global matrices, solving systems of linear equations, and common pitfalls in space discretization and time integration.