Finite element space
====================

Given a computational domain :math:`\Omega` covered by a simplicial
mesh :math:`\mathcal{T}_h(\Omega)`, the space :math:`V_h(\Omega)` of
:math:`\mathbb{P}_1`-Lagrange finite element functions is the set of
continuous piecewise affine functions i.e. defined as

      :math:`V_h(\Omega):=\lbrace v_h\in \mathcal{C}^{0}(\overline{\Omega}),v_h\vert_{\tau}\in \mathbb{P}_1(\tau)\;\forall \tau\in \mathcal{T}_h(\Omega)\rbrace`
	    
      :math:`\mathbb{P}_1(\tau):=\lbrace \varphi\vert_{\tau}, \varphi(\mathbf{x}) = \alpha\cdot\mathbf{x}+\beta, \alpha\in \mathbb{R}^d,\beta\in\mathbb{R}\rbrace`

In the code `femtool`, such a vector space is modelled by an object of
type ``FeSpace``.  In terms of data members, this object consists of a
``Mesh mesh_`` and a dynamically allocated array of size the number of
element in `mesh_`. Each cell of this dynamically allocated array
stores the numbers of the degrees of freedom local to the
corresponding mesh cell.

.. doxygenclass:: FeSpace
   :members: