I did try looking at the documentation for FEValuesViews::Vector 
dim, spacedim >::hessian(const unsigned int shape_function, const unsigned 
int q_point)  before coming here, and all it provides is

"Return the Hessian (the tensor of rank 2 of all second derivatives) of the 
vector components selected by this view, for the shape function and 
quadrature point selected by the arguments."

I looked in fe_values.h to see if it was commented in the implementation 
and all that I see there is

  hessian_type return_value; 
  for (unsigned int d=0; d 
<dim; ++d 
    if (shape_function_data[shape_function].
         = fe_values->finite_element_output.shape_hessians[

which I'm not quite sure how to parse. The comments in the header file only 
say "same as for the scalar case except that we have one more index." (the 
added index is d).

This is why I brought my question here. 

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