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readme.txt

+#########################
+#  author: T.Tscherpel  #
+#  created 04/07/2023   #
+#########################
+
+This file contains supplementary material for the article 
+	DIMENSIONS OF EXACTLY DIVERGENCE-FREE FINITE ELEMENT SPACES IN 3D
+	by L. R. SCOTT AND T. TSCHERPEL
+	published in [...]
+
+#########################
+
+main file: meshquantities.py 
+	to be run with FEniCS (dolfin)
+	
+	generation of 2 types of meshes:
+            mesh1 (regular mesh of unit cube) and
+            mesh2 (diamond mesh), with scaling factor s = 20
+		figure(1): 	plot of mesh1
+		saved files: 	"cube_mesh.png", "cube_mesh.tex" (tikz)
+		figure(2): 	plot of mesh2 
+		saved files: 	"diamond_mesh.png", "diamond_mesh.tex" (tikz)
+	
+	uniform refinement 
+		figure(3): 	plot of ebar over v for uniformly refined meshes
+		saved files: 	"ebar_unif.tex" (tikz), "ebar_unif.png"
+	
+	adaptive refinement (58 times)
+		figure(4): 	plot of ebar over v for adaptively refined meshes with
+                                refinement point refpt = [.1111111,.33333333,0.33333333]
+		saved files: 	"ebar_adapt.tex" (tikz), "ebar_adapt.png"
+
+#########################	
+	
+list of subroutines
+
+	meshcube(iR,s)	
+    		# input: iR initial refinement, s scaling factor leading to cube [0,s]^3
+    		# output: regular mesh of unit cube 
+    
+	meshdiamond(m,s)
+    		# input: m number of tetrahedra on the spine, s scaling factor for the whole mesh
+    		# output: mesh of a diamond domain with spine vertices (0,0,s) and (0,0,-s) and
+                          equator vertices on the circle with radius s, with 2m tetrahedra
+    		
+    	meshquant(mesh):
+    		# input: mesh
+    		# output: v number of vertices, e number of edges 
+    		
+	ebar(mesh,ind,maxref,vmax,refpt):
+    		# input: mesh, ind indicator for uniform (0) or adaptive (1) refinement,
+                         refmax maximal number of refinements, 
+		  	 vmax maximal number of vertices, refpt point for adaptive refinement 
+    		# output: vlist list of vertices, ebarlist list of ebar values of the mesh thats
+                          arises by uniform or adaptive refinements from the inout mesh 
+
+	adaptiveref(mesh,refpt):
+		# soubtourine of ebar
+    		# input:     mesh, refpt point towards which adaptive refinement is performed
+    		# output:    refined mesh (using Carey-Plaza refinement)
+