The Finite Element Method in 2D

Abstract

In this chapter we develop finite element methods for numerical solution of partial differential equations in two dimensions. The approach taken is the same as before, that is, we first rewrite the equation in variational form, and then seek an approximate solution in the space of continuous piecewise linear functions. Although the numerical methods presented are general, we focus on linear second order elliptic equations with the Poisson equation as our main model problem. We prove basic error estimates, discuss the implementation of the involved algorithms, and study some examples of application.