* freedom values as given by the input
* vector; they are not weighted by the
* area of cells, i.e. the mean is
- * computed as <tt>sum_i v_i</tt>, rather
- * than as <tt>int_Omega v(x) = int_Omega
- * sum_i v_i phi_i(x)</tt>.
+ * computed as $\sum_i v_i$, rather than
+ * as $\int_\Omega v(x) = \int_\Omega
+ * \sum_i v_i \phi_i(x)$. The latter can
+ * be obtained from the
+ * VectorTools::compute_mean_function,
+ * however.
*
* Apart from the vector @p v to operate
* on, this function takes a bit
* This function integrates the
* chosen component over the
* whole domain and returns the
- * result.
- *
- * Subtracting this mean value
- * from the node vector does not
- * generally yield the desired
- * result of a finite element
- * function with mean value
- * zero. In fact, it only works
- * for Lagrangian
- * elements. Therefore, it is
- * necessary to compute the mean
- * value and subtract it in the
- * evaluation routine.
+ * result, i.e. it computes
+ * $\int_\Omega [u_h(x)]_c \; dx$
+ * where $c$ is the vector component
+ * and $u_h$ is the function
+ * representation of the nodal
+ * vector given as fourth
+ * argument. The integral is evaluated
+ * numerically using the quadrature
+ * formula given as third argument.
*
- * So far, this is needed only in
- * the error evaluation for
- * Stokes with complete Dirichlet
- * boundaries for the velocities.
+ * This function is used in the
+ * "Possibilities for extensions" part of
+ * the results section of @ref step_3
+ * "step-3".
+ *
+ * @note The function is most often used
+ * when solving a problem whose solution
+ * is only defined up to a constant, for
+ * example a pure Neumann problem or the
+ * pressure in a Stokes or Navier-Stokes
+ * problem. In both cases, subtracting
+ * the mean value as computed by the
+ * current function, from the nodal
+ * vector does not generally yield the
+ * desired result of a finite element
+ * function with mean value zero. In
+ * fact, it only works for Lagrangian
+ * elements. For all other elements, you
+ * will need to compute the mean value
+ * and subtract it right inside the
+ * evaluation routine.
*/
template <int dim, class InVector, int spacedim>
static double compute_mean_value (const Mapping<dim, spacedim> &mapping,
const unsigned int component);
/**
- * Calls the compute_mean_value()
+ * Calls the other compute_mean_value()
* function, see above, with
* <tt>mapping=MappingQ1@<dim@>()</tt>.
*/