ABSTRACT
Having discussed the fundamental concepts underlying the formulation and implementation of the Galerkin finite element method in one spatial dimension, we proceed to extend the methodology to two dimensions. The generalized framework developed in this chapter will allow us to build algorithms for solving the Laplace equation, the Poisson equation, the unsteady heat conduction equation, the convection equation, the convection-diffusion equation, the equations of linear elasticity in solid mechanics, and the equations of viscous flow in hydrodynamics. In the discourse, we will demonstrate one of the most powerful features of the finite element method, which is the ability to accommodate solution domains with arbitrary and even complex geometry.
