\begin{tikzpicture}[
	scale=1.5,
	coarse/.style={circle,draw=gray,inner sep=4},
	fine/.style={cross out,draw=gray,inner sep=2},
	ibase/.style={coarse,draw=black,very thick},
	wantedfine/.style={fine,draw=black,ultra thick},
	arrow/.style={-{Latex[length=2mm]},thick}
]

\foreach \x in {-1,...,3}
	\foreach \y in {-1,...,2}
		\node[coarse] at (\x,\y){ };

\foreach \x in {0,...,8}
	\foreach \y in {-2,...,4}
		\node[fine] at (2+\x*0.5,\y*0.5){ };

\node[wantedfine] at (2,0.5){ };
\node[ibase] at (2,2){ };
\node[ibase] at (2,1){ };
\node[ibase] at (2,0){ };
\node[ibase] at (2,-1){ };

\draw[dashed,very thick] (1.8,-1.2) rectangle (2.2,2.2);
\draw[dashed,draw=gray] (2.8,-1.2) rectangle (3.2,2.2);

\draw[arrow] (2,3.3) node[right] {Interpolation von grob nach fein, \(\U_{g \to f}\)} -- (2,2.3);
\draw[arrow] (3,2.8) node[right] {Restriktion von fein nach grob, \(\U_{f \to g}\)} -- (3,2.3);

\draw[decorate,decoration={brace,amplitude=10pt,mirror},line width=1pt]
(1.8,-1.4) -- (3.2,-1.4) node[midway,below,yshift=-6pt] {Übergangsbereich};
\end{tikzpicture}