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Commit 1abe566d authored by Felix Schindler's avatar Felix Schindler
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added missing latex stuff

git-svn-id: https://dune.mathematik.uni-freiburg.de/svn/dune-fem-functionals/trunk@4 4028485c-44d9-4cde-a312-5a4635ee2db9
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@Article{DKNO10,
author = {Dedner, A. and Kl\"ofkorn, R. and Nolte, M. and Ohlberger, M.},
title = {A generic interface for parallel and adaptive discretization schemes: abstraction principles and the Dune-Fem module},
journal = {Computing},
number = {3-4},
volume = {90},
pages = {165--196},
year = {2010},
publisher = {Springer},
doi = {10.1007/s00607-010-0110-3},
url = {/2010/DKNO10},
}
\ No newline at end of file
[General]
def_graphic_ext=
img_extIsRegExp=false
img_extensions=.eps .jpg .jpeg .png .pdf .ps .fig .gif
kileprversion=2
kileversion=2.0.85
lastDocument=dune-fem-functionals.tex
masterDocument=
name=dune fem functionals
pkg_extIsRegExp=false
pkg_extensions=.cls .sty .bbx .cbx .lbx
src_extIsRegExp=false
src_extensions=.tex .ltx .latex .dtx .ins
[Tools]
MakeIndex=
QuickBuild=
[document-settings,item:dune-fem-functionals.tex]
Bookmarks=
Encoding=UTF-8
Highlighting=LaTeX
Indentation Mode=normal
Mode=LaTeX
ReadWrite=true
[item:dune-fem-functionals.bib]
archive=true
column=0
encoding=
highlight=
line=0
mode=
open=false
order=-1
[item:dune-fem-functionals.tex]
archive=true
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encoding=UTF-8
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File added
......@@ -18,7 +18,36 @@
\usepgflibrary{arrows}
\input{dunemacros}
% spaces after macros but not when . or , or something is following
\usepackage{xspace}
\usepackage{listings}
\lstset{language=C++,basicstyle=\ttfamily}
% dune core modules
\newcommand{\dune}{\textsc{Dune}\xspace}
\newcommand{\dunecommon}{\textsc{Dune-Common}\xspace}
\newcommand{\dunegrid}{\textsc{Dune-Grid}\xspace}
\newcommand{\duneistl}{\textsc{Dune-Istl}\xspace}
\newcommand{\dunelocalfunctions}{\textsc{Dune-Localfunctions}\xspace}
% external modules
\newcommand{\dunefem}{\textsc{Dune-Fem}\xspace}
\newcommand{\dunepdelab}{\textsc{Dune-PDELab}\xspace}
\newcommand{\dumux}{\textsc{DuMu}$^\textrm{x}$\xspace}
% external packages
\newcommand{\alugrid}{\textsc{ALUGrid}\xspace}
\newcommand{\alberta}{\textsc{ALBERTA}\xspace}
% grid names
\newcommand{\albertagrid}{{\tt AlbertaGrid}\xspace}
\newcommand{\alusimplexgrid}{{\tt ALUSimplexGrid}\xspace}
\newcommand{\alucubegrid}{{\tt ALUCubeGrid}\xspace}
\newcommand{\aluconformgrid}{{\tt ALUConformGrid}\xspace}
\newcommand{\uggrid}{{\tt UGGrid}\xspace}
\newcommand{\onedgrid}{{\tt OneDGrid}\xspace}
\newcommand{\sgrid}{{\tt SGrid}\xspace}
\newcommand{\yaspgrid}{{\tt YaspGrid}\xspace}
\numberwithin{equation}{section}
......@@ -67,9 +96,9 @@
We start with an overview on the mathematical concept which is carried over to a corresponding programming concept. The following notations and definitions are required for the subsequent sections.
\begin{definition}[Function and Functionspace]\theoremNewline
If $\Omega$ denotes a subset of $\mathbb{R}^n$, a mapping $v : \Omega \rightarrow \mathbb{R}^d $ is called a \textnormal{function}. Any vector space $V$ which only consits functions is called a \textnormal{functionspace}. If additionally
If $\Omega$ denotes a subset of $\mathbb{R}^n$, a mapping $v : \Omega \rightarrow \mathbb{R}^d $ is called a \textnormal{function}. Any vector space $V$ which only consits functions is called a \textnormal{functionspace}. If additionally
\begin{align*}
(\alpha v_1 + \beta v_2) \in V \enspace \forall v_1,v_2 \in V, \forall \alpha,\beta \in \R
(\alpha v_1 + \beta v_2) \in V \enspace \forall v_1,v_2 \in V, \forall \alpha,\beta \in \R
\end{align*}
the space is called a \textnormal{linear functionspace}.
\end{definition}\theoremEndLine
......@@ -125,7 +154,7 @@ We start with an overview on the mathematical concept which is carried over to a
an \textnormal{operator} on $V_g$.
\end{definition}\theoremEndLine
In the subsequent sections, we are dealing with the following problem:
In the subsequent sections, we are dealing with the following problem:
\begin{problem}
For a linear space $V$, a linear (constraint) subspace $V_C$, a functional $F$ and an affine subspace $V_g$ of $V$, find $u \in V_g$ with
......@@ -185,7 +214,7 @@ First of all we give an overview on the various classes that are required in our
\item[$\circ$] at first, we restrict ourselves to linear functionals
\item[$\circ$] we might distinguish the types of functionals according to the codim: CodimFunctionals, for example {\tt FunctionalType::CodimFunctional<codim>}; combinations of functionals for different codims must be possible (for instance $F(\Phi) = \int_{\Omega} f \Phi + \int_{\partial \Omega} g \Phi$)
\item[$\circ$] required methods:
\item[$\cdot$] method: {\tt apply( function )} $\leftrightarrow$ $F[ v ]$, $v$ analytical function
\item[$\cdot$] method: {\tt apply( function )} $\leftrightarrow$ $F[ v ]$, $v$ analytical function
\item[$\cdot$] method: {\tt apply( discreteFunction )} $\leftrightarrow$ $F[v_H]$, $v_H$ discrete function
\item[$\cdot$] method: {\tt applyLocal( localBasefunctionSet )} $\rightarrow$ an abstract method depending on the specific realisation of a functional; we can say it returns a vector of local contributions for a specific grid element; it is required for assembling the right hand side in our system of equations; details are given later
\end{itemize}
......@@ -201,7 +230,7 @@ First of all we give an overview on the various classes that are required in our
\item[$\circ$] other methods depending on the specific type of a constraint (e.g. DirichletConstraint)?
\item[$\circ$] constraints are used to construct a 'constraint subspace' - for the user, nothing else has to be done with the constraints
\end{itemize}
{\tt typedef LinearSubspace < DiscreteFunctionSpace, ConstraintType >
{\tt typedef LinearSubspace < DiscreteFunctionSpace, ConstraintType >
\hspace{1pt}LinearSubspaceType;}
\begin{itemize}
......@@ -558,7 +587,7 @@ Example: {\tt ConstraintType::DirichletConstraint dirConstraint( function );}
\bibliographystyle{plain}
\bibliography{bibliography}
\bibliography{dune-fem-functionals}
\end{document}
......
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