## Authors

Frédéric Hecht
Olivier Pironneau
Antoine Le Hyaric
Kohji Ohtsuka (Web master of this site(CoMFoS)) Examples

## 1 Introduction

Installation, How to use FreeFem++, Environment variables, and the init file, History

## 2 Getting Started

FEM by FreeFem++ : how does it work?, Some Features of FreeFem++, The Development Cycle,

## 3 Learning by Examples

Membranes, Heat Exchanger, Acoustics, Thermal Conduction, Irrotational Fan Blade Flow and Thermal effects, Pure Convection, A Projection Algorithm for the Navier-Stokes equations, The System of elasticity, The System of Stokes for Fluids, A Large Fluid Problem, An Example with Complex Numbers, Optimal Control, A Flow with Shocks, Classification of the equations

## 4 Syntax

Data Types, List of major types, Global Variables, System Commands, Arithmetic, One Variable Functions, Functions of Two Variables, Arrays, Loops, Input/Outpu, Exception handling,

## 5 Mesh Generation

Commands for Mesh Generation, Boundary FEM Spaces Built as Empty Meshes, Remeshing, Regular Triangulation: hTriangle, Adaptmesh, Trunc, Splitmesh, Meshing Examples, How to change the label, Mesh in 3d, Meshing Example (3d),

## 6 Finite Elements

Lagrange finite element, P1 Nonconforming Element, Other FE-space, Vector valued FE-function, A Fast Finite Element Interpolator, Keywords: Problem and Solve, Parameters affecting solve and problem, Problem definition, Numerical Integration, Variational Form, Sparse Matrix, PDE Data Vector, Interpolation matrix, Finite elements connectivity

## 7 Visualization

Plot, link with gnuplot, link with medit,

## 9 Mathematical Models

Static Problems, Elasticity, Nonlinear Static Problems, Eigenvalue Problems, Evolution Problems, Navier-Stokes Equation, Variational inequality, Domain decomposition， Schwarz Overlap Scheme, Fluid/Structures Coupled Problem, Transmission Problem, Free Boundary Problem, Nonlinear elasticity Compressible Neo-Hookean Materials: Computational Solutions

## 10 Parallel version experimental

Schwarz in parallel

## 11 Mesh Files

File mesh data structure, bb File type for Store Solutions, BB File Type for Store Solutions, Metric File, List of AM FMT, AMDBA Meshes

## 12 Add new finite element

Some notation, Which class of add

## Appendix

### A Table of Notations

Generalities, Sets, Mappings, Matrices, Vectors, Numbers, Differential Calculus, Meshes, Finite Element Spaces

### B Grammar

The bison grammar, The Types of the languages, and cast, All the operators

### C Dynamical link

A first example myfunction.cpp, Example Discrete Fast Fourier Transform, Load Module for Dervieux’ P0-P1 Finite Volume Method, Add a new finite element, Add a new sparse solver Keywords