Dear Franck,

It looks like you're passing the flag "update_normal_vectors" to an 
FEValues object, which is not sensible as it is used only for volume 
calculations (as opposed to surface calculations). I think that this is the 
propogation of the flags that leads to the issue:


         DarcySystem<dim>  (darcy_fe, quadrature_formula, 
face_quadrature_formula,
                            (update_values|update_normal_vectors|  // 
<---------- Initially created here
                             update_quadrature_points|
                             update_JxW_values|
                             update_gradients),
                             saturation_fe,
                             update_values),

      template <int dim>
      DarcySystem<dim>::
      DarcySystem (const FiniteElement<dim> &darcy_fe,
                   const Quadrature<dim>    &darcy_quadrature,
                   const Quadrature<dim-1>  &darcy_face_quadrature,
                   const UpdateFlags        darcy_update_flags,  <---- 
Contains update_normal_vectors
                   const FiniteElement<dim> &saturation_fe,
                   const UpdateFlags        saturation_update_flags)
      :
        DarcyPreconditioner<dim> (darcy_fe, darcy_quadrature,
                                  darcy_update_flags, // <-------- Oops... 
contains 
update_normal_vectors
                                  saturation_fe,
                                  saturation_update_flags),

        darcy_fe_face_values (darcy_fe, darcy_face_quadrature, 
darcy_update_flags),  // <---- Presumably this is correct



     template <int dim>
      DarcyPreconditioner<dim>::
      DarcyPreconditioner  (const FiniteElement<dim>  &darcy_fe,
                            const Quadrature<dim>     &darcy_quadrature,
                            const UpdateFlags         darcy_update_flags,
                            const FiniteElement<dim>  &saturation_fe,
                            const UpdateFlags         
saturation_update_flags)
        :
        darcy_fe_values (darcy_fe, darcy_quadrature, darcy_update_flags),  
<----- Initialised with same flags for  darcy_fe_face_values

You probably need to split this flag into two sets, or simply add on the 
"update_normal_vectors" flag when you initialise  darcy_fe_face_values.

I hope that this was indeed the issue, and that what I've listed above 
helps resolve it.

Best,
Jean-Paul

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