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revision 2646 by jfenwick, Fri Sep 4 00:13:00 2009 UTC revision 2647 by gross, Fri Sep 4 05:25:25 2009 UTC
# Line 50  PDE solutions on the \Domain \var{mydoma Line 50  PDE solutions on the \Domain \var{mydoma
50  \begin{python}  \begin{python}
51    solution_space=Solution(mydomain)    solution_space=Solution(mydomain)
52  \end{python}  \end{python}
53  The following generators for function spaces on a \Domain \var{mydomain} are available:  The following generators for function spaces on a \Domain \var{mydomain} are commonly used:
54  \begin{itemize}  \begin{itemize}
55  \item \var{Solution(mydomain)}: solutions of a PDE.  \item \var{Solution(mydomain)}: solutions of a PDE.
56  \item \var{ReducedSolution(mydomain)}: solutions of a PDE with a reduced smoothness requirement.    \item \var{ReducedSolution(mydomain)}: solutions of a PDE with a reduced smoothness requirement.  
# Line 60  The following generators for function sp Line 60  The following generators for function sp
60  \item \var{FunctionOnContact0(mydomain)}: functions on side $0$ of the discontinuity.  \item \var{FunctionOnContact0(mydomain)}: functions on side $0$ of the discontinuity.
61  \item \var{FunctionOnContact1(mydomain)}: functions on side $1$ of the discontinuity.  \item \var{FunctionOnContact1(mydomain)}: functions on side $1$ of the discontinuity.
62  \end{itemize}  \end{itemize}
63    In some cases under-integration is used. For these cases the user may use a
64    \FunctionSpace from the floowing list:
65    \begin{itemize}
66    \item \var{ReducedFunction(mydomain)}
67    \item \var{ReducedFunctionOnBoundary(mydomain)}
68    \item \var{ReducedFunctionOnContact0(mydomain)}
69    \item \var{ReducedFunctionOnContact1(mydomain)}
70    \end{itemize}
71    In comparison to the full teh corresponding full version
72    they use a reduced number of integration nodes (typically one only) to represent values.
73    
74    
75  The reduced smoothness for PDE solution is often used to fulfill the Ladyzhenskaya–-Babuska–-Brezzi condition \cite{LBB} when  The reduced smoothness for PDE solution is often used to fulfill the Ladyzhenskaya–-Babuska–-Brezzi condition \cite{LBB} when
76  solving saddle point problems \index{saddle point problems}, eg. the Stokes equation.  solving saddle point problems \index{saddle point problems}, eg. the Stokes equation.

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