Split, expand refinement method overview section

Mainly expand on grid discretization and overlap characterization.

4 files changed, 42 insertions, 0 deletions

diff --git a/img/coinciding_grid.tikz b/img/coinciding_grid.tikz
new file mode 100644
index 0000000..d4273e3
--- /dev/null
+++ b/img/coinciding_grid.tikz
@@ -0,0 +1,12 @@
+\begin{tikzpicture}[
+	scale=1.0,
+	fine/.style={circle,draw=black,thick,inner sep=2},
+]
+
+\draw[step=1.0,black] (0.75,0.75) grid (6.25,6.25);
+\draw[step=0.5,gray,thin] (2,2) grid (5,5);
+
+\foreach \x in {0,...,6}
+	\foreach \y in {0,...,6}
+		\node[fine] at (2+0.5*\x,2+0.5*\y){ };
+\end{tikzpicture}
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}
diff --git a/img/refined_poiseuille_1.png b/img/refined_poiseuille_1.png
new file mode 100644
index 0000000..fee3996
--- /dev/null
+++ b/img/refined_poiseuille_1.png
diff --git a/img/staggered_grid.tikz b/img/staggered_grid.tikz
new file mode 100644
index 0000000..d77b055
--- /dev/null
+++ b/img/staggered_grid.tikz
@@ -0,0 +1,12 @@
+\begin{tikzpicture}[
+	scale=1.0,
+	fine/.style={circle,draw=black,thick,inner sep=2},
+]
+
+\draw[step=1.0,black] (0.75,0.75) grid (6.25,6.25);
+\draw[step=0.5,gray,thin,xshift=1.75cm,yshift=1.75cm] (0,0) grid (3.5,3.5);
+
+\foreach \x in {0,...,7}
+	\foreach \y in {0,...,7}
+		\node[fine] at (1.75+0.5*\x,1.75+0.5*\y){ };
+\end{tikzpicture}