Dear All,
I still have some problem in solving my equations on a curved domain
(sphere in 3D or circle in 2D). I got error with this content:
invalid initialization of reference of type ‘dealii::Triangulation<2, 3>&’
from expression of type ‘dealii::Triangulation<3, 3>’
Does it mean that I should use different codim for my domain and Finite
element spaces because of the fact that I should solve my problem and
impose my boundary condition on a sphere.
Thanks,
Benhour
On Wednesday, October 19, 2016 at 4:43:59 PM UTC-5, Wolfgang Bangerth wrote:
>
> > In fact, I should solve my problem on a sphere (circle). According to
> your
> > noteworthy comments, the only thing that I have to do is change the
> geometry
> > and use higher order mapping for accuracy. Another thing is that
> consider a
> > half of a circle in r-z coordinate system and the problem is
> axisymmetric.
> > what should be my boundary condition for rotation axis (z-coordinate)?
>
> That depends on the equation, but if you were, for example, solving the
> Laplace equation in cylindrical coordinates, then there would be no
> special
> boundary condition along the z-axis (at r=0). That's because you will find
> that when you do the integration by parts, you get boundary terms of the
> form
>
> \int_{\partial \Omega} n.nabla u(r,z) varphi(r,z) 2*pi*r dr dz
>
> But at the symmetry axis, r=0, so the integrand disappears at the
> boundary.
>
> In other words, for most equations, there is nothing special you need to
> do at
> the symmetry axis.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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