diff --git a/readme.txt b/readme.txt new file mode 100644 index 0000000000000000000000000000000000000000..b222ccebe210f9efecb5ed970a3b5b9d437425d3 --- /dev/null +++ b/readme.txt @@ -0,0 +1,61 @@ +######################### +# 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) +