ABSTRACT
One alternative discretization method is the finite element method (FEM), and it can be used on non-rectangular domains in both 2D and 3D. This chapter introduces the FEM with linear shape functions and examines its applications. The FEM can be formulated from either minimization principles (variational) or weak equations (Galerkin). The general discretization of the weak formulation is based on the Rayleigh–Ritz approximation. The chapter introduces a study of the MATLAB code fem2d.m, which includes the simple test case and two applications. The first application is to heat transfer in a cooling fin attached to a steam pipe. In the second application we return to ideal fluid flow, but now the flow is about a non-rectangular obstacle. The chapter dscusses upwind finite difference method for flow of a pollutant in a stream. It describes Lax–Wendroff methods for classes of differential equations.
