FreeFem++, a tool to solve PDEs numerically

Georges Sadaka (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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++.

Mots clés: FreeFem++; finite element method; heat equation; poisson equation; elliptic equation; non linear equation; rate of convergence

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Georges Sadaka. FreeFem++, a tool to solve PDEs numerically. 2012. ⟨hal-00694787⟩