FreeFem++, a tool to solve PDEs numerically

Abstract: FreeFem++ is an open source platform to solve partial differential equations numerically, based on finite element methods. It was developed at the Laboratoire Jacques-Louis Lions, Universit\'e Pierre et Marie Curie, Paris by Fr\'ed\'eric Hecht in collaboration with Olivier Pironneau, Jacques Morice, Antoine Le Hyaric and Kohji Ohtsuka. The FreeFem++ platform has been developed to facilitate teaching and basic research through prototyping. FreeFem++ has an advanced automatic mesh generator, capable of a posteriori mesh adaptation; it has a general purpose elliptic solver interfaced with fast algorithms such as the multi-frontal method UMFPACK, SuperLU . Hyperbolic and parabolic problems are solved by iterative algorithms prescribed by the user with the high level language of FreeFem++. It has several triangular finite elements, including discontinuous elements. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. We will give in the sequel an introduction to FreeFem++ which include the basic of this software. You may find more information throw this link http://www.freefem.org/ff++.