* to the destination cell, i.e. the
* unrefined one, while the column indices
* are for the refined cell's degrees of
- * freedom.
+ * freedom. The application of this matrix
+ * is therefore usually its being
+ * multiplied by the vector of nodal values
+ * on the child.
*
* In essence, using the matrices from the
* children to the mother cell amounts to
* contributions of each child into the
* nodal value vector of the mother cell.
*
+ * While we could avoid this and rather add
+ * up the contributions of each child for
+ * nodes that are interior of the mother
+ * cell, we can't for nodes on the boundary
+ * of the mother cell. The reason for this
+ * is that we know how many children may
+ * contribute to the interpolated nodal
+ * value of an interior degree of freedom.
+ * However, we don't know for dofs on the
+ * boundary, for which we only know how many
+ * children from each side of the face
+ * contribute, but we would have to look out
+ * of the cell to know how many neighbors
+ * there are and then, still, we would have
+ * to have two different interpolation
+ * routines for local interpolation and for
+ * the contribution of a cell to a global
+ * interpolation if we wanted to compute
+ * that by adding up local contributions.
+ *
+ * Because of this problem, we chose to
+ * write rather than add the contributions
+ * of each cell to the interpolation onto
+ * the mother cell. However, there now is
+ * another problem which appears when using
+ * discontinuous finite elements. The
+ * process of 'writing' assumed that we
+ * get the same result for each degree of
+ * freedom from each of the children, such
+ * that 'over'writing would not destroy
+ * information; when using discontinuous
+ * elements, this assumption is violated.
+ *
+ * SOLUTION? NOT YET MADE UP!
+ *
* To compute the interpolation of a
* finite element field to a cell, you
* may use the #get_interpolated_dof_values#