$F(v_1, v_2,\nabla v_3)\cdot\nabla u$&\texttt{Vec2Grad\_FOT\footnote[1]{* available on request}}($v_1,v_2,v_3\in${\scriptsize DOFVector}$\langle\mathbb{R}\rangle$, $F:\mathbb{R}\times\mathbb{R}\times\mathbb{R}^n\rightarrow\mathbb{R}^n$) \\
\item All operators are listed in the files \texttt{ZeroOrderTerm.h}, \texttt{FirstOrderTerm.h} and \texttt{SecondOrderTerm.h}.
\item The following definitions/shortcuts are used to reduce typing:
$L_2$-Scalar product: $\langle\cdot,\cdot\rangle$, trialfunction: $\phi$, testfunction $\psi$, coefficients $c\in\mathbb{R},\;\vec{1},\vec{b},\vec{x}\in\mathbb{R}^n,$ with $(\vec{1})_i =1$, $B\in\mathbb{R}^{n\times n}$, functors $f:(\ldots)\rightarrow\mathbb{R}$, $F:(\ldots)\rightarrow\mathbb{R}^n$ and $A:(\ldots)\rightarrow\mathbb{R}^{n\times n}$.
\item Some mathematical notations are used to describe data-structures: $\mathbb{R}$ means \texttt{double}, $\mathbb{R}^n$ means \texttt{WorldVector<double>} and $\mathbb{R}^{n\times n}$ means \texttt{WorldMatrix<double>}.
\item$f, F, A$ can be implemented as \texttt{(*)AbstractFunction$\langle$ReturnType, InputType1, InputType2, ...$\rangle$}, where \texttt{(*)}$\in$\{$\emptyset$, \texttt{Binary}, \texttt{Tertiary}, \texttt{Quart}\} depending on the number of input arguments.
\item The data-structure \texttt{DOFVector<*>} is always a pointer to a DOFVector.
\item Optional arguments are depicted in square brackets $[*]$, where constants $c =1$ by default, functions are \texttt{NULL}-pointers by default and are treated as identity functors or simple multiplication functors.
\item The argument $div:=\mathbb{R}^{n\times n}\rightarrow\mathbb{R}^n$ is only interesting for error estimators and optional. Is should implement the divergence of the matrix function in the operator.
\item The argument \small{vec}$\langle*\rangle$ should be implemented as \texttt{std::vector$\langle*\rangle$}.
\item In the last Second-Order-Operator \texttt{GeneralParametric\_SOT}, the second argument $\vec{n}$ to $A$ is the elementnormal, especially for surface meshes.