Short course on numerical methods for PDEs: An introduction to Freefem++,

Abstract

The nite element method is a technique very useful to obtain approximate solutions to boundary-value problems. The method envolves the creation of an mesh, dividing the domain of the solution into a finite number of a simple subdomains, the nite elements, and uses the variational concepts to construct an approximation of the solution over the collection of finite elements. FreeFem++, as the name suggest, is a free software written in C++, with own high level programming language which is not too far from the mathematical writing of the problems, based on the Finite Element Method to solve differential equations of parcial derivatives with boundary-values. With a advanced automatic mesh generator and the high level user friendly input language, offers us a large variety of nite elements types and a considerable set of solvers for the linear systems. The visualisation of the results is to distance of command plot, but its possible to link with gnoplot and medit, from the script, and obtain plots with more quality for publish purpose. This short course has a goal to do an introduction to Freefem++, giving some simple tools to new users.