Hows, Whys and Wherefores of FEM in Quantitative Finance - VI

In the last blog post we discussed the 2D triangular element - a preparation for the next posts of our series. Today we start with the variational formulation of a two dimensional static diffusion-reaction equation.

An element's contribution to the system of equations is given by

where A denotes the element's area and N is the row vector containing the element's shape functions. In A Workout in Computational Finance the derivation of the final equations is explained in detail. At this point we only give the final result of the derivation (neglecting surface integrals)

This equation can be written in a more compact form

In the finite element world, K is named element stiffness matrix, M is named element mass matrix and f is called the element load vector.

This series of blog posts summarizes a chapter of the book A Workout in Computational Finance

The seventh post of the series will be published on Thursday, July 18 (also enthusiastic blog authors need some holiday) and will give a deeper analysis of the derived element matrices in general and will calculate them for the concrete example of the 2D linear triangular element presented in the last post.