How to do adaptive refinement respecting a curved boundary?

Question

Suppose I want to solve a problem using auto-adaptivity on a disc or other domain with curved boundary. I start with a coarse mesh which approximates the disc by a polygon with a fairly small number of sides. As the mesh is refined I would like new nodes to be added to the circular boundary, not to the initial polygonal approximation of it, so the final domain on which the solution is computed on is very close to the disk, not to the initial polygon. Is this possible?

Answer 1

Unfortunately, since dolfin doesn't have any knowledge of the underlying geometry of the mesh it can not automatically adapt to a curved boundary. One can however manually refine a mesh and then snap points back to a given boundary. See, demo/undocumented/smoothing/python/demo_smoothing.py in the dolfin repository where this is shown for a circular hole inside a rectangular mesh.

Comments

Yes, thanks, this is a good alternative if one knows how much one wants to refine near the curved boundary, and so doesn't need adaptivity. Unfortunately snapping to the boundary doesn't play well with adaptivity, in the sense that if you generate an adaptive mesh and then snap the points back to the boundary, there will be artifacts in the mesh due to the corners that were present on the boundary during the adaptive process (before they were snapped to the curve). It would be nice if there were an easy way to apply the snap_boundary method after each step of the adaptive process.