diff --git a/examples/thermal_edge_flow/study12.geo b/examples/thermal_edge_flow/study12.geo
index 5e0d51e0261aa15082f500a5bce4155f01a97dd7..13b8fbf769d6f4040d62f64a325f22431b883641 100644
--- a/examples/thermal_edge_flow/study12.geo
+++ b/examples/thermal_edge_flow/study12.geo
@@ -27,20 +27,23 @@ res8 = 2^-split * 2^-10; // inner edge leftbot
 res9 = 2^-split * 2^-2; // inner bulk middle
 
 
+
 Point(1001) = {0.0, 0.0, 0, res1};
 Point(1002) = {2.0, 0.0, 0, res4};
 Point(1003) = {4.0, 0.0, 0, res1};
-Point(1004) = {8.0-dist1, 0.0, 0, res3};
-Point(1005) = {8.0, 0.0, 0, res3};
-Point(1006) = {8.0, 0.0+dist1, 0, res3};
-Point(1007) = {8.0, 8.0-dist1, 0, res3};
-Point(1008) = {8.0, 8.0, 0, res3};
-Point(1009) = {8.0-dist1, 8.0, 0, res3};
-Point(1010) = {0.0+dist1, 8.0, 0, res3};
-Point(1011) = {0.0, 8.0, 0, res3};
-Point(1012) = {0.0, 8.0-dist1, 0, res3};
-Point(1013) = {0.0, 4.0, 0, res1};
-Point(1014) = {0.0, 2.0, 0, res4};
+Point(1004) = {4.5, 0.0, 0, res3};
+Point(1005) = {8.0-dist1, 0.0, 0, res3};
+Point(1006) = {8.0, 0.0, 0, res3};
+Point(1007) = {8.0, 0.0+dist1, 0, res3};
+Point(1008) = {8.0, 8.0-dist1, 0, res3};
+Point(1009) = {8.0, 8.0, 0, res3};
+Point(1010) = {8.0-dist1, 8.0, 0, res3};
+Point(1011) = {0.0+dist1, 8.0, 0, res3};
+Point(1012) = {0.0, 8.0, 0, res3};
+Point(1013) = {0.0, 8.0-dist1, 0, res3};
+Point(1014) = {0.0, 4.5, 0, res3};
+Point(1015) = {0.0, 4.0, 0, res1};
+Point(1016) = {0.0, 2.0, 0, res4};
 
 Point(1101) = {0.0+dist1, 0.0+dist1, 0, res7};
 Point(1102) = {4.0, 0.0+dist1, 0, res7};
@@ -81,6 +84,13 @@ Point(1502) = {3.5, 0.5, 0, res9};
 Point(1503) = {3.5, 3.5, 0, res9};
 Point(1504) = {0.5, 3.5, 0, res9};
 
+Point(1601) = {4.5, 0.5, 0, res2};
+Point(1602) = {7.5, 0.5, 0, res2};
+Point(1603) = {7.5, 7.5, 0, res2};
+Point(1604) = {0.5, 7.5, 0, res2};
+Point(1605) = {0.5, 4.5, 0, res2};
+Point(1606) = {4.5, 4.5, 0, res2};
+
 
 Line(2001) = {1001, 1002};
 Line(2002) = {1002, 1003};
@@ -95,7 +105,9 @@ Line(2010) = {1010, 1011};
 Line(2011) = {1011, 1012};
 Line(2012) = {1012, 1013};
 Line(2013) = {1013, 1014};
-Line(2014) = {1014, 1001};
+Line(2014) = {1014, 1015};
+Line(2015) = {1015, 1016};
+Line(2016) = {1016, 1001};
 
 
 Line(2101) = {1101, 1102};
@@ -139,20 +151,28 @@ Circle(2602) = {1203, 1304, 1205};
 Circle(2603) = {1206, 1307, 1208};
 Circle(2604) = {1209, 1310, 1211};
 
+Line(2701) = {1601, 1602};
+Line(2702) = {1602, 1603};
+Line(2703) = {1603, 1604};
+Line(2704) = {1604, 1605};
+Line(2705) = {1605, 1606};
+Line(2706) = {1606, 1601};
+
 
 Curve Loop(3207) = {2202, 2602, 2205, 2603, 2208, 2604, 2211, 2601};
 Curve Loop(3208) = {2301:2312};
 Plane Surface(4207) = {3207, 3208};
 Curve Loop(3209) = {2105, 2106, 2101, 2102, 2103, 2104};
-Curve Loop(3210) = {2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2001};
+Curve Loop(3210) = {2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2001};
 Plane Surface(4209) = {3210, 3209};
 Curve Loop(3211) = {2102, 2103, 2104, 2105, 2401, 2402, 2403, 2404};
-Plane Surface(4210) = {3211};
 Curve Loop(3212) = {2101, -2404, -2403, -2402, -2401, 2106};
 Curve Loop(3213) = {2501:2504};
 Plane Surface(4211) = {3212, 3213};
 Plane Surface(4212) = {3213, 3207};
-
+Curve Loop(3214) = {2701:2706};
+Plane Surface(4210) = {3211,3214};
+Plane Surface(4213) = {3214};
 
 Physical Curve("outer",3000) = {
   2001:2014
@@ -167,7 +187,8 @@ Physical Surface("mesh",4000) = {
   4209,
   4210,
   4211,
-  4212
+  4212,
+  4213
 };
 
 Mesh.Algorithm = 6;