Split, expand refinement method overview section

Mainly expand on grid discretization and overlap characterization.

1 files changed, 18 insertions, 0 deletions

diff --git a/img/invalid_overlap_area.tikz b/img/invalid_overlap_area.tikz
new file mode 100644
index 0000000..f8ad72b
--- /dev/null
+++ b/img/invalid_overlap_area.tikz
@@ -0,0 +1,18 @@
+\begin{tikzpicture}[
+	scale=1.5,
+	coarse/.style={circle,draw=black,thick,inner sep=4},
+	fine/.style={cross out,draw=black,thick,inner sep=2},
+	arrow/.style={-{Latex[length=2mm]},thick}
+]
+
+\foreach \x in {-1,...,3}
+	\foreach \y in {0,...,2}
+		\node[coarse] at (\x,\y){ };
+
+\foreach \x in {0,...,8}
+	\foreach \y in {0,...,4}
+		\node[fine] at (1.5+\x*0.5,\y*0.5){ };
+
+\draw[arrow] (1.5,2.8) node[right] {Feine Knoten in \(\partial D_f \not\subset \partial D_g^\circ\)} -- (1.5,2.3);
+\draw[dashed,thick] (1.3,-0.2) rectangle (1.7,2.2);
+\end{tikzpicture}