# Mesh a hollow cylinder

Questions seems to be simple answerde, but in Mathemtica v11.0.1 I didn't find a solution

Needs["NDSolveFEM"];
scheibe =ParametricRegion[{  r Cos[\[CurlyPhi]], r Sin[\[CurlyPhi]],
z}, {{r, 1/2, 1}, {\[CurlyPhi], 0, 2 Pi}, {z, -1, 1}}];
RegionPlot3D[scheibe, Boxed -> False]


The region scheibe is ok but meshing

ToElementMesh[scheibe]
DiscretizeGraphics [scheibe]


fails in both cases.

What could be the reason? Is there a workaround? Thanks.

The purpose behind my question is, I want to solve poisson equation in cylindrical coordinates in a predefined mesh.

• The first case using ToElementMesh works for me Mathematica 12.0 running on a Mac. Try: scheibemesh = ToElementMesh[scheibe]; scheibemesh["Wireframe"]. The second attempt using DiscretizeGraphics doesn't work as this function can only discrete 3D graphics primitives or give approximations to certain types of non-linear primitives. This means that Parametric regions cannot be converted into a mesh using this second method as I understand. Maybe others can help as to why the first doesn't work. – Dunlop Aug 23 '19 at 11:25
• BoundaryDiscretizeRegion[ RegionProduct[Line[{{-1}, {1}}], Annulus[{0, 0}, {1/2, 1}]]] might serve as alternative. – Henrik Schumacher Aug 23 '19 at 11:48
• @HenrikSchumacher Thanks, this gives me a boundary mesh, which might be transformed to 3D mesh... – Ulrich Neumann Aug 23 '19 at 12:07
• @Dunlop Thanks, it seems to be a version problem (ToElementMesh, v11) Perhaps I'll find workaround to get a 3Dmesh – Ulrich Neumann Aug 23 '19 at 12:09

ToElementMesh[scheibe]["Wireframe"]

• @UlrichNeumann, I do not have 11.0.1 installed, but maybe something like this: ToElementMesh[RegionProduct[Annulus[], Line[{{0}, {1}}]]]["Wireframe"] – user21 Aug 26 '19 at 9:27