# How to use FEM to solve a PDE

I come from a Computer Science background and I've been around searching for a concise tutorial that tells me how Finite Element Method is used to solve a certain partial differential equation. Unfortunately I was depressed with the large number of advanced studies and papers that assumed prior knowledge.

Is it possible to understand the entire process of implementing FEM easily?

• It might be expeditious for you to say a bit more about the "certain partial differential equation" you want to solve. The FEM is fairly simply applied to elliptic linear PDE's in a modest number of dimensions, but if your case is not of this form, then it's probably best to explain that now. BTW a "Computer Science background" suggests you are familiar with discrete mathematics and linear algebra in particular. If that is not the case, also worth some clarificiation. – hardmath Nov 30 '11 at 16:13
• Thank you. Well, the equation I want to solve is the [dynamic version of Euler-Bernoulli beam equation](en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation#Dynamic beam equation) which is $\cfrac{\partial^2 }{\partial x^2}\left(EI\cfrac{\partial^2 w}{\partial x^2}\right) = - \mu\cfrac{\partial^2 w}{\partial t^2} + q(x)$. (sorry for the long reply due to problems in my country) – al-Amjad Tawfiq Isstaif Jan 3 '12 at 10:41
• Just glancing at it, this doesn't seem to be of elliptic type, though it is a linear PDE. I'm assuming constants $E,I,\mu$ are positive. You should also have some boundary/initial conditions specified. If it is of hyperbolic type (as I suspect), then you may still be able to give a FEM approximation, though typically one might apply a finite element approach in the "space" variable and a finite difference stepping approach in the "time" dimension. – hardmath Jan 3 '12 at 16:09