Improve text on the LocalView concept

doc/manual/dune-functions-manual.tex

@@ -971,41 +971,41 @@ basis which can, e.g., be used to check validity in a static assertion.
 \end{lstlisting}
 
 \subsection{User interface of a \cpp{LocalView}}
-We will now continue with the description of the interface
-of a local view as returned by \cpp{GlobalBasis::localView()}.
-Since a \cpp{LocalView} is not meant to be constructed
-manually, there is no interface for this. Instead, a \cpp{LocalView}
-can be obtained from the global basis via the \cpp{localView()}
-method. As a consequence the global basis of type \cpp{GlobalBasis}
-is known and exported by the \cpp{globalBasis()} method.
 
+The \cpp{LocalView} concept represents the localization of a basis tree to a single element.
+\cpp{LocalView} objects are returned by the method \cpp{GlobalBasis::localView()}.
+There is no way to construct such objects directly.
+The global basis of type \cpp{GlobalBasis}
+is known by the \cpp{LocalView} object, and exported by the \cpp{globalBasis()} method.
 \begin{lstlisting}
-class LocalView
-{
-public:
   using GlobalBasis = <implementation defined>;
   const GlobalBasis& globalBasis() const;
 \end{lstlisting}
 
-A local view is meant to provides access to all basis
+A local view provides access to all basis
 functions whose support has nontrivial intersection with
-a given element. These will be called \emph{local basis functions}
-in the following. To achieve this, the local view must
-first be bound to this element by calling \cpp{bind(Element)}.
+a given element (the \emph{local basis functions}).
+To achieve this, the local view must
+first be bound to this element by calling
+\begin{lstlisting}
+  using GridView = typename GlobalBasis::GridView;
+  using Element = typename GridView::template Codim<0>::Entity;
+  void bind(const Element& e);
+\end{lstlisting}
 This call may incorporate expensive computations needed to
 setup the those local basis functions. The local view can be
 bound to another element by calling this method again.
 To set the local view to unbound state again, you
-can call the \cpp{unbind()} method.
+can call the
+\begin{lstlisting}
+void unbind();
+\end{lstlisting}
+method.
 Notice that the local view will store a copy of the bound
 element that is accessible via \cpp{element()}.
-
 \begin{lstlisting}
-  using GridView = typename GlobalBasis::GridView;
   using Element = typename GridView::template Codim<0>::Entity;
-  void bind(const Element& e);
   const Element& element() const;
-  void unbind();
 \end{lstlisting}
 
 The total number of basis functions associated to the
@@ -1040,6 +1040,7 @@ given below.
   const Tree& tree() const;
 \end{lstlisting}
 
+\todosander{Siehe oben: Für den Krams zu Teilraumbasen würde ich ein separates Unterkapitel einführen.}
 In order to be consistent with a \cpp{SubspaceBasis::LocalView}
 the additional method \cpp{rootLocalView()} returns the local view
 itself.