]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Augment documentation.
authorWolfgang Bangerth <bangerth@math.tamu.edu>
Sun, 17 May 2009 13:20:52 +0000 (13:20 +0000)
committerWolfgang Bangerth <bangerth@math.tamu.edu>
Sun, 17 May 2009 13:20:52 +0000 (13:20 +0000)
git-svn-id: https://svn.dealii.org/trunk@18862 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/deal.II/include/numerics/vectors.h

index f8a82086064303b0f5f2383f261c33a8e81475cc..21e5af0e844d5f235ad6ec24ddf77fc9372db02a 100644 (file)
@@ -1703,9 +1703,12 @@ class VectorTools
                                      * 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
@@ -1729,24 +1732,37 @@ class VectorTools
                                      * 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,
@@ -1756,7 +1772,7 @@ class VectorTools
                                      const unsigned int     component);
 
                                     /**
-                                     * Calls the compute_mean_value()
+                                     * Calls the other compute_mean_value()
                                      * function, see above, with
                                      * <tt>mapping=MappingQ1@<dim@>()</tt>.
                                      */

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