[firedrake] problems with importing a mesh

[G. D. McBain]

> 2) For splines, I have also removed the point (updated code below) and when I look at it using gmsh I see that some points aren't actually on the boundary.  This does seem odd but I am not sure how to fix it.   Should I use a different kind of spline?

The problem may be this: the Gmsh concept of Physical versus Elementary entities.

http://gmsh.info/doc/texinfo/gmsh.html#Elementary-vs-physical-entities

Your Gmsh file has only Elementary entities (Point, Line/Spline, Line Loop, Plane Surface).  The trick is to mark the domain (for this two-dimensional problem) as a Physical Surface and each part of the boundary as a Physical Line.  In three dimensions, those would be Physical Volume and Physical Surface, respectively.

When a Gmsh file has no Physical entities, Gmsh puts everything into the mesh, including construction points (centres of arcs, control-points of splines), which often end up as disconnected, but if there is a least one Physical entity, only those finite elements belonging to Physical entities are included in the output .msh.

A quirk of Firedrake, maybe inherited from PETSc which I think it uses to read Gmsh meshes, is that every part of the boundary has to be declared as part of a Physical Line/Surface, even if it's only going to get homogeneous natural boundary conditions in the finite element problem.

Hope this helps; I can supply a little example, if the above is unclear.
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