1. Nodal Projection

An important keyword is project which allows to compute the interpolant of an expression with respect to a nodal function space over a part of the mesh or the whole mesh. The interface is as follows

project( _space=<nodal function space in which the interpolant lives>
         _range=<domain range iterators>,
         _expr=<expression to be interpolated>, .... )

Here are some examples:

typedef FunctionSpace<Mesh<Simplex<$d$>,
                      bases<Lagrange<1,Vectorial> > > Xhv_type;
auto Xhv = Xhv_type::New( mesh );
// build a piecewise $\P_1$ vectorial function in Xhv containing the
// coordinates of the vertices the mesh.
auto coord = project( _space=Xhv, _range=elements(mesh), _expr=P() );
// compute the x derivative of the coord function
auto dx_coord = project( _space=Xhv, _range=elements(mesh), _expr=dxv(coord) );
auto dy_coord = project( _space=Xhv, _range=elements(mesh), _expr=dyv(coord) );

2. Projection Operator

A projection operator is available that supports:

  • L_2 projection

  • H_1 projection