## Introduction
Feel++ is a C++ library for arbitrary order Galerkin methods (e.g. finite and spectral element methods ) continuous or discontinuous in 1D 2D and 3D. The objectives of this framework is quite ambitious; ambitions which could be express in various ways such as :
 - the creation of a versatile mathematical kernel solving easily problems using different techniques thus allowing testing and comparing methods, e.g. cG versus dG,
 - the creation of a small and manageable library which shall nevertheless encompass a wide range of numerical methods and techniques,
 - build mathematical software that follows closely the mathematical abstractions associated with partial differential equations (PDE)
 - the creation of a library entirely in C++ allowing to create C++ complex and typically multi-physics applications such as fluid-structure interaction or mass transport in haemodynamic

Some basic installation procedure are available in the INSTALL.org file.

## Documentation

 - [Feel++ Online Reference Manual](http://feelpp.github.io/feelpp/)

## Features
 - 1D 2D and 3D (including high order) geometries and also lower topological dimension 1D(curve) in 2D and 3D or 2D(surface) in 3D
 - continuous and discontinuous arbitrary order Galerkin Methods in 1D, 2D and 3D including finite and spectral element methods
 - domain specific embedded language in C++ for variational formulations
 - interfaced with [PETSc](http://www.mcs.anl.gov/petsc/) for linear and non-linear solvers
 - seamless parallel computations using PETSc
 - interfaced with [SLEPc](http://www.grycap.upv.es/slepc/) for large-scale sparse standard and generalized eigenvalue  solvers
 - supports [Gmsh](http://www.geuz.org/gmsh) for mesh generation
 - supports [Gmsh](http://www.geuz.org/gmsh) for post-processing (including on high order geometries)
 - supports [Paraview](http://www.paraview.org) for post-processing


## Examples

### Laplacian in 2D using P3 Lagrange basis functions

Here is a full example to solve $-\Delta u = f in \Omega,\quad u=g on \partial \Omega$

```
#include <feel/feel.hpp>

int main(int argc, char**argv )
{
    using namespace Feel;
	Environment env( _argc=argc, _argv=argv,
                     _desc=feel_options(),
                     _about=about(_name="qs_laplacian",
                                  _author="Feel++ Consortium",
                                  _email="feelpp-devel@feelpp.org"));

    auto mesh = unitSquare();
    auto Vh = Pch<1>( mesh );
    auto u = Vh->element();
    auto v = Vh->element();

    auto l = form1( _test=Vh );
    l = integrate(_range=elements(mesh),
                  _expr=id(v));

    auto a = form2( _trial=Vh, _test=Vh );
    a = integrate(_range=elements(mesh),
                  _expr=gradt(u)*trans(grad(v)) );
    a+=on(_range=boundaryfaces(mesh), _rhs=l, _element=u,
          _expr=constant(0.) );
    a.solve(_rhs=l,_solution=u);

    auto e = exporter( _mesh=mesh, _name="qs_laplacian" );
    e->add( "u", u );
    e->save();
    return 0;
}
```


### Bratu equation in 2D

Here is a full non-linear example - the Bratu equation - to solve $-\Delta u +
e^u = 0 in \Omega,\quad u=0 on \partial \Omega$.

```
#include <feel/feel.hpp>

inline
Feel::po::options_description
makeOptions()
{
    Feel::po::options_description bratuoptions( "Bratu problem options" );
    bratuoptions.add_options()
    ( "lambda", Feel::po::value<double>()->default_value( 1 ), 
                "exp() coefficient value for the Bratu problem" )
    ( "penalbc", Feel::po::value<double>()->default_value( 30 ), 
                 "penalisation parameter for the weak boundary conditions" )
    ( "hsize", Feel::po::value<double>()->default_value( 0.1 ), 
               "first h value to start convergence" )
    ( "export-matlab", "export matrix and vectors in matlab" )
    ;
    return bratuoptions.add( Feel::feel_options() );
}

/**
 * Bratu Problem
 *
 * solve \f$ -\Delta u + \lambda \exp(u) = 0, \quad u_\Gamma = 0\f$ on \f$\Omega\f$
 */
int
main( int argc, char** argv )
{

    using namespace Feel;
	Environment env( _argc=argc, _argv=argv,
                     _desc=makeOptions(),
                     _about=about(_name="bratu",
                                  _author="Christophe Prud'homme",
                                  _email="christophe.prudhomme@feelpp.org"));
    auto mesh = unitSquare();
    auto Vh = Pch<3>( mesh );
    auto u = Vh->element();
    auto v = Vh->element();
    double penalbc = option(_name="penalbc").as<double>();
    double lambda = option(_name="lambda").as<double>();

    auto Jacobian = [=](const vector_ptrtype& X, sparse_matrix_ptrtype& J)
        {
            auto a = form2( _test=Vh, _trial=Vh, _matrix=J );
            a = integrate( elements( mesh ), gradt( u )*trans( grad( v ) ) );
            a += integrate( elements( mesh ), lambda*( exp( idv( u ) ) )*idt( u )*id( v ) );
            a += integrate( boundaryfaces( mesh ), 
               ( - trans( id( v ) )*( gradt( u )*N() ) - trans( idt( u ) )*( grad( v )*N()  + penalbc*trans( idt( u ) )*id( v )/hFace() ) );
        };
    auto Residual = [=](const vector_ptrtype& X, vector_ptrtype& R)
        {
            auto u = Vh->element();
            u = *X;
            auto r = form1( _test=Vh, _vector=R );
            r = integrate( elements( mesh ), gradv( u )*trans( grad( v ) ) );
            r +=  integrate( elements( mesh ),  lambda*exp( idv( u ) )*id( v ) );
            r +=  integrate( boundaryfaces( mesh ),
               ( - trans( id( v ) )*( gradv( u )*N() ) - trans( idv( u ) )*( grad( v )*N() ) + penalbc*trans( idv( u ) )*id( v )/hFace() ) );
        };
    u.zero();
    backend()->nlSolver()->residual = Residual;
    backend()->nlSolver()->jacobian = Jacobian;
    backend()->nlSolve( _solution=u );

    auto e = exporter( _mesh=mesh );
    e->add( "u", u );
    e->save();
}
```