Re: [Libmesh-users] Constraint matrix

[Roy S. <roy...@ic...>]

On Sat, 6 Jan 2018, Renato Poli wrote:

> Hi again, I am trying to close this issue here, but got into trouble again.
>
> Is there a common way to tie a dof against the derivative of other dofs.

Not really.  For one thing, there's no such thing as a spatial
derivative of a dof.  You can get the spatial derivative of a variable
at *some* places in a typical finite element solution, but not
everywhere, and in particular not at the vertices (where your
lowest-order C0 dofs will be located!).

> My primary variables are 'pressure' and 'displacement' and I need to
> tie pressure to stress (C du/dx)?
> I can imagine using more dofs in the "constraint_row" (the element
> ones, which are summed together to get the derivative), but I am
> afraid of getting an unstable system.

You could get the dof coefficients corresponding to a du/dx (get dphi
for each shape function at the point where you want a gradient
evaluation, take the x component of each) and insert them into a
constraint row, but this is not likely to be the most accurate way to
solve your problem.  Not sure what you're solving (contact?  porous
media flow?) but there's probably a formulation out there somewhere
which enforces a pressure-strain relationship weakly rather than with
point-by-point constraint equations.
---
Roy