> Unfortunately, visualizing is not enough to my purposes. I need the
> tangential component of the gradient at the mesh faces to perform a
> post-processing phase where I compute some relevant quantities to be used
> later in solving a different problem.
>
In general, you can create a quadrature rule that has support points at
face centers on the reference cell [0,1]^{dim}, i.e.
std::vector<Point<dim-1> > reference_face_centers(1);
reference_face_center[0] = Point<1> (.5) //2d
reference_face_center[0] = Point<1> (.5, .5) //3d
//fill reference_face_centers
Quadrature<dim>(reference_face_centers);
Then, create at FEFaceValues object using that Quadrature and a vector to
store the gradient:
FEValues<dim> fe_dummy_values(fe, reference_face_centers,
update_gradients | update_normal_vectors);
std::vector<Tensor<1,dim> > gradient (1);
and loop over all cells and faces as shown in step-7[1]. Finally, you can
query the location of the quadrature point and the gradient via
fe_face_values.reinit (cell, face_number);
fe_face_values.get_function_gradients(solution, gradient)
std::cout << "The gradient at " << fe_face_values.quadrature_point(0) <<
" is " << gradient[0] << std::endl;
std::cout << "The normal vector at " <<
fe_face_values.quadrature_point(0) << " is " <<
fe_face_values.normal_vector(0) << std::endl;
Alternatively, you can compute the projection of your discrete solution
into the FE_Nedelec<dim>(0) space by solving for u satisfying
(v,u)=(v, \nabla solution) for all v in FE_Nedelec<dim>(0)
For doing that, you would need to define an additional FE_Nedelec object,
create a mass matrix and evaluate the gradient of your original solution
at the quadrature points you are using for building the mass matrix via
fe_values.get_function_gradients(...).
Which way the more appropriate one is depends on how exactly you want to
perform postprocessing.
Best,
Daniel
[1] https://www.dealii.org/8.4.0/doxygen/deal.II/step_7.html
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