[Gmsh] about .mesh file format

[Geordie McBain]

2010/7/23 Felipe Montefuscolo <felipe.mt87 at gmail.com>:
> hi again, thanks for the answer.
> Let-me explain my problem with a example. If I make a cube, I can
> label the faces (with Physical groups) that are on the boundary so that all
> nodes that are in
> these faces will be labeled too. Perfect, that's what I want, because
> with this I can impose the Dirichlet boundary conditions in my fem code.
> The problem is: and nodes that are in the corners of the cube ? these nodes
> belong to three faces that may have different labels, and how to decide
> which
> face does he live ? that is why it would be desirable to add a label to them
> in medit file.
> This detail can deteriorate a solution of a lid-driven cavity problem, for
> example.

Thanks for the clarification.  I see the issue.

A lot of finite element programs (e.g. libMesh, FreeFem++) actually
impose Dirichlet conditions as Robin conditions with very high
`conductances' between the solution at the boundary and what it should
be.  This makes all the boundary conditions `natural' and none
`essential'.  It means you don't need to worry about which nodes are
on Dirichlet boundaries, because none are.  This technique is
described in e.g.

Becker, E. B., G. F. Carey, & J. T. Oden (1981). Finite Elements, An
Introduction, Volume 1 of The Texas Finite Element Series. Englewood
Cliffs, New Jersey: Prentice-Hall, pp. 121--122

Ern, A., & J.-L. Guermond (2004). Theory and Practice of Finite
Elements, Volume 159 of  Applied Mathematical Sciences. New York:
Springer, section 8.4.4, pp. 379--380

but of course you might not want to do this, I know.

I can't really think of a way to impose true Dirichlet conditions on
corners a mesh defined by a MEDIT .mesh mesh file, because of this
restriction of one tag per node... Actually here's a hack: for nodes
on just one patch it's easy enough, as you've worked out.  For nodes
on an intersection of two (or more) patches, can you define that
intersection as another patch and give it a special tag, meaning that
any node with that tag is actually on each of the patches?