How to calculate the absolute value of a form in the weak form

UFL
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1

Hello,

I’m solving the Maxwell equations, in Maxwell equations, there is a Gauss law:
Screenshot from 2024-04-10 17-33-53
so I need to calculate the error regarding the Gauss law, in DOLFINX, I can easily do:

abs(div(E)-rho)*dx

but the term E is usually defined in some curl space, so div(E) is not well-posed and I can not calculate it in the strong form, then I would like to calculate the gauss error in the weak form, like:

abs(E*div(v)+rho*v)*dx
where v is the test function.

But it seems like the function abs can not be used when I have the test function in the form, and I got the error:

raise ArityMismatch("Applying nonlinear operator {0} to expression depending on form argument {1}.".format(o._ufl_class_.__name__, t))
ufl.algorithms.check_arities.ArityMismatch: Applying nonlinear operator Abs to expression depending on form argument v_0.

Does anyone know what I could do in this case?

Thanks!

2

So your v is in another space than E (say DG-0?) to make it well-posed?

As the error message states, you cannot have an abs around a test function.

I would compute the integrated error (without abs) and then in turn add the abs for each entry of the corresponding vector.
An alternative way to solve this is by sending E*div(v)+rho*v into a dolfinx.fem.Expression, eval at your specified quadrature points, and do a manual assembly where you add the abs for each term.