Sorry for pestering you, but why does this not happen in 
"grid-2-single-refine.svg" and "grid-3-coarse.svg"?

On Monday, April 18, 2022 at 9:05:42 PM UTC+5:30 Wolfgang Bangerth wrote:

> On 4/16/22 21:40, ankit tyagi wrote:
> > *** Caution: EXTERNAL Sender ***
> > 
> > I think the issue is different here. PFA three files corresponding to
> > a coarser version of grid-2 mesh. First is the original coarse mesh,
> > second with single refinement, and third with two refinements. The
> > first refinement doesn't cause any issue, but second does. In the
> > first refinement, all cells are inner cells, so appropriate changes
> > are made to all the boundaries. But in the second refinement, there
> > are outer cells and inner cells, and only the inner cells are
> > refined. This causes a contradiction, because the outer and inner
> > cells share a boundary: the middle circle. Because of refinement of
> > inner cells, they get a new outer boundary, but the outer cells retain
> > their inner boundary, creating discontinuities at the middle circle.
> > 
> > This point is further proved if we change the refinement strategy to
> > the one mentioned in the "Possibilities for extensions" section.  This
> > time, all the cells with center lying on the positive y side,
> > are refined . Even though boundaries are still curved, it causes no
> > issue. PFA "grid-3-coarse.svg" and full code also.
>
> I see no contradiction to my earlier statements. The only edges that are 
> affected by the use of a curved manifold description are the ones that are 
> in 
> circumferential direction, and in your pictures, these are exactly the 
> ones 
> that have the funny appearance. The manifold is chosen in such a way that 
> all 
> radial edges are in fact straight, and so whenever there is a hanging node 
> along such an edge, the two child edges geometrically cover the parent 
> edge 
> exactly.
>
> Best
> W.
>
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>

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