* Implementation of Hierarchical finite elements @p{Qp} that yield the
* finite element space of continuous, piecewise polynomials of degree
* @p{p}. This class is realized using tensor product polynomials
- * based on a hierarchical basis of the interval @p{[-1,1]} suitable
- * for building an @p{hp} tensor product finite element. There are not
- * many differences between @p{FE_Q_Hierarchical} and @p{FE_Q}, except
- * that we now allow the degree to be nonconstant for @p{p}-refinement.
+ * based on a hierarchical basis @p{Hierarchical} of the interval
+ * @p{[0,1]} which is suitable for building an @p{hp} tensor product
+ * finite element, if we assume that each element has a single degree.
+ *
+ * There are not many differences between @p{FE_Q_Hierarchical} and
+ * @p{FE_Q}, except that we add a function @p{embedding_dofs} that takes
+ * a given integer @p{q}, between @p{1} and @p{p}, and
+ * returns the numbering of basis functions of the element of order
+ * @p{q} in basis of order @p{p}. This function is
+ * useful if one wants to make calculations using the hierarchical
+ * nature of these shape functions.
+ *
+ * The unit support points now are reduced to @p{0}, @p{1}, and @p{0.5} in
+ * one dimension, and tensor products in higher dimensions. Thus, various
+ * interpolation functions will only work correctly for the linear case.
+ * Future work will involve writing projection--interpolation operators
+ * that can interpolate onto the higher order bubble functions.
+ *
+ * The various constraint, prolongation, and restriction matrices are
+ * now available in all dimensions for all degrees @p{p}, currently up to
+ * order 19.
*
* The constructor of this class takes the degree @p{p} of this finite
* element.
* polynomials of degree @p{p}. This @p{TensorProductPolynomials}
* object provides all values and derivatives of the shape functions.
*
- * Furthermore the constructor filles the @p{interface_constraints},
- * the @p{prolongation} (embedding) and the @p{restriction}
- * matrices. These are implemented only up to a certain degree, that
- * is listed in the following: (fix this eventually......)
- *
- * @begin{itemize}
- * @item @p{dim==1}
- * @begin{itemize}
- * @item the @p{interface_constraints} are not needed
- * @item the @p{prolongation} matrices up to degree 4, and
- * @item the @p{restriction} matrices up to degree 4.
- * @end{itemize}
- * @item @p{dim==2}
- * @begin{itemize}
- * @item the @p{interface_constraints} up to degree 4,
- * @item the @p{prolongation} matrices up to degree 3, and
- * @item the @p{restriction} matrices up to degree 4.
- * @end{itemize}
- * @item @p{dim==3}
- * @begin{itemize}
- * @item the @p{interface_constraints} up to degree 2,
- * @item the @p{prolongation} matrices up to degree 2, and
- * @item the @p{restriction} matrices up to degree 4.
- * @end{itemize}
- * @end{itemize}
- *
* @sect3{Numbering of the degrees of freedom (DoFs)}
*
* The original ordering of the shape functions represented by the
* beginning with the shape functions whose support points are at the
* vertices, then on the line, on the quads, and finally (for 3d) on
* the hexes. To be explicit, these numberings are listed in the
- * following: (support points for @p{hp}??)
+ * following:
*
* @sect4{Q1 elements}
* @begin{itemize}