Finite Element Methods

The finite element method is a numerical method for solving partial differential equations (PDEs), and has become particularly popular in engineering and physics. This chapter presents most important concepts used for grid generation, refinement strategies and adaptivity. It deals with the shape functions for one‐, two‐ and three‐dimensional elements. The chapter focuses on assembling process of a linear system of equations using the discrete finite elements. This procedure is shown in a step‐by‐step manner by applying the finite element method to a two‐dimensional static diffusion‐reaction equation. Finally, the chapter compares the numerical results for the price of a zero coupon bond with face amount 1 and different life times obtained by the use of standard finite elements, finite elements with streamline diffusion, and the analytical solution under the two factor Hull‐White interest rate model with constant model parameters.