Najwa:
I know that merge triangulation in deal.ii will not work properly if there are
hanging nodes ( unmatching of the meshes at the interface).
My question is, what if I have to have this hanging node? Is there a way I can
work it out, or are there any other suggestions I should try?
The issue is that if you merge two triangulations, the assumption is that
*all* cells are part of the coarse mesh. If you have a hanging node on one
side, say in a situation like this:
*--* *---*
| | | |
*--X + | |
| | | |
*--* *---*
then you end up with a coarse mesh of three cells in which the top and bottom
vertex of the common interfaces are identified between the two parts, and the
middle node is not. So you have a "crack" in your domain: an internal
boundary. This cannot be avoided because hanging nodes, *by definition* are
along interfaces between cells *of different refinement level*. But here, all
cells are at refinement level zero.
The ideal approach would of course be to avoid the situation altogether. If
you can't do that, you have to enforce continuity along the "crack" in a
different way, for example by manually adding constraints for the node marked
by X above. Alternatively, you can enforce continuity along the crack weakly,
like in discontinuous Galerkin approaches. It turns out that there is a
tutorial program that actually shows something like this: step-33 (see the
section on "Adaptivity").
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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