of the nodes that are subject to Dirichlet boundary conditions where the
solution is forced to equal $u_i = g_i = g(\mathbf{x}_i)$ as the interpolation
of boundary values on the Dirichlet-constrained node points $i\in \mathcal
-N_D$. In this formula, where we have assumed that the degrees of freedom are
-numbered such that the ones subject to a Dirichlet condition are all appended
-to the end of the list of degrees of freedom. We then insert this solution
+N_D$. We then insert this solution
representation into the weak form, e.g. the Laplacian shown above, and move
the known quantities to the right hand side:
@f{eqnarray*}
with $i\in N \setminus \mathcal N_D$ that are not related to the nodes
constrained by Dirichlet conditions.
-In the implementation in deal.II, the integrals $(\varphi_i,\varphi_j)_\Omega$
+In the implementation in deal.II, the integrals $(\nabla \varphi_i,\nabla \varphi_j)_\Omega$
on the right hand side are already contained in the local matrix contributions
we assemble on each cell. When using
ConstraintMatrix::distributed_local_to_global() as first described in the