From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Sat, 18 Apr 2015 02:33:52 +0000 (-0500)
Subject: Also enable computing the H_div seminorm.
X-Git-Tag: v8.3.0-rc1~233^2~3
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=16f19226bfcdfb1bd3abcc52318168ace8042050;p=dealii.git

Also enable computing the H_div seminorm.

This is joint work with Zhen Tao and Arezou Ghesmati.
---

diff --git a/doc/news/changes.h b/doc/news/changes.h
index 9d05c3c281..b955d28707 100644
--- a/doc/news/changes.h
+++ b/doc/news/changes.h
@@ -473,6 +473,13 @@ inconvenience this causes.
   <br>
   (Lei Qiao, 2015/04/19)
   </li>
+  
+  <li> New: The VectorTools::integrate_difference() function can now
+  also compute the $H_\text{div}$ seminorm, using the
+  VectorTools::NormType::Hdiv_seminorm argument.
+  <br>
+  (Zhen Tao, Arezou Ghesmati, Wolfgang Bangerth, 2015/04/17)
+  </li>
 
   <li> New: TrilinosWrappers::BlockSparseMatrix now has member functions
   TrilinosWrappers::BlockSparseMatrix::domain_paritioner() and
@@ -480,7 +487,6 @@ inconvenience this causes.
   vector of the underlying block Epetra_Map.
   <br>
   (Matthias Maier, 2015/04/08)
-
   </li>
 
   <li> Fixed: The class SymmetricTensor<2,dim> is now usable also for dim>3.
diff --git a/include/deal.II/numerics/vector_tools.h b/include/deal.II/numerics/vector_tools.h
index 77c8958e71..a35cbd384a 100644
--- a/include/deal.II/numerics/vector_tools.h
+++ b/include/deal.II/numerics/vector_tools.h
@@ -355,6 +355,10 @@ namespace VectorTools
      * #L2_norm of the gradient.
      */
     H1_seminorm,
+    /**
+     * #L2_norm of the divergence of a vector field
+     */
+    Hdiv_seminorm,
     /**
      * The square of this norm is the square of the #L2_norm plus the square
      * of the #H1_seminorm.
@@ -1802,7 +1806,12 @@ namespace VectorTools
    * formula only evaluates the two solutions at these particular points,
    * choosing this quadrature formula may indicate an error far smaller than
    * it actually is.
-   * @param[in] norm The norm $X$ shown above that should be computed.
+   * @param[in] norm The norm $X$ shown above that should be computed. If
+   *   the norm is NormType::Hdiv_seminorm, then the finite element on which this
+   *   function is called needs to have at least dim vector components,
+   *   and the divergence will be computed on the first div components.
+   *   This works, for example, on the finite elements used for the
+   *   mixed Laplace (step-20) and the Stokes equations (step-22).
    * @param[in] weight The additional argument @p weight allows to evaluate
    * weighted norms.  The weight function may be scalar, establishing a
    * spatially variable weight in the domain for all components equally. This
diff --git a/include/deal.II/numerics/vector_tools.templates.h b/include/deal.II/numerics/vector_tools.templates.h
index 919cd6db2e..77e7605a48 100644
--- a/include/deal.II/numerics/vector_tools.templates.h
+++ b/include/deal.II/numerics/vector_tools.templates.h
@@ -6278,6 +6278,24 @@ namespace VectorTools
           diff = std::sqrt(diff);
           break;
 
+        case Hdiv_seminorm:
+          for (unsigned int q=0; q<n_q_points; ++q)
+            {
+              Assert (n_components >= dim,
+                      ExcMessage ("You can only ask for the Hdiv norm for a finite element "
+                                  "with at least 'dim' components. In that case, this function "
+                                  "will take the divergence of the first 'dim' components."));
+              double sum = 0;
+              // take the trace of the derivatives, square it, multiply it
+              // with the weight function
+              for (unsigned int k=0; k<dim; ++k)
+                sum += (data.psi_grads[q][k][k] * data.psi_grads[q][k][k]) *
+                       data.weight_vectors[q](k);
+              diff += sum * fe_values.JxW(q);
+            }
+          diff = std::sqrt(diff);
+          break;
+
         case W1infty_seminorm:
         case W1infty_norm:
         {
@@ -6336,6 +6354,7 @@ namespace VectorTools
         case L2_norm:
         case H1_seminorm:
         case H1_norm:
+        case Hdiv_seminorm:
           exponent = 2.;
           break;
 
@@ -6352,6 +6371,7 @@ namespace VectorTools
       switch (norm)
         {
         case H1_seminorm:
+        case Hdiv_seminorm:
         case W1p_seminorm:
         case W1infty_seminorm:
           update_flags |= UpdateFlags (update_gradients);