Phani,

> I have a general query. Is there anything I should be particularly careful 
> when I have to handle non-homogenous dirichlet boundary on a mesh with 
> hanging nodes on the boundary? I am working in the matrix-free data 
> structure format. I am trying to impose non-homogenous boundary conditions 
> on the non-hanging nodes using static condensation and allowing the hanging 
> nodes to be handled using its hanging node constraint equation without 
> treating it explicitly as a boundary nodes.
>
Have a look at the newest version of the documentation of step-37 
<https://www.dealii.org/developer/doxygen/deal.II/step_37.html#InhomogeneousDirichletboundaryconditions>.
 
There is a special section talking about inhomogeneous boundary conditions 
in the MatrixFree framework.
In general, treating homogeneous boundary conditions should not be a 
problem, but you have to be careful about inhomogeneous ones.

Best,
Daniel

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