Giovanna,
I have tried defining a more general function as a list of points and
> values associated with those points (using vector_value_list). This
> definition is based on the output of another simulation (with
> post-processing of the solution gradient at the boundary). I used the
> vertices located along the boundary as list of points. I don't know if it
> makes sense.
>
> I have attached the relevant parts of code below. I have two main
> questions:
> - Are there specific points where the function should be defined? (For
> instance the face Gauss points along the boundary)
>
The function will set strong boundary conditions for the normal component.
Hence, you will need to provide the values at the mapped dof_support_points
of the boundary cells.
The approach you are taking here for providing these values is rather
expensive but might not be avoidable easily. At least you should be able to
initialize listNodes and listValues in the constructor of the class so you
don't have to create it each time you are for some values anew.
> - I get an error of dimensions mismatch (also copied below), could you
> help me understand the reason? I am solving the problem in 2D
>
You are missing to initialize the base class Function<dim> with dim
components, i.e. you need to write a constructor for your BoundaryValues
class that looks like
BoundaryValues () : Function<dim>(dim)
{}
The default value is one component but you need dim ones.
Best,
Daniel
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