Yann,
you did not read my email. The approach to compute the norm of the
residual goes through *integration with FEValues*, not with computing
nodal values. You are stuck thinking about how the approach you are
trying to use can be made to work; but the approach you are using is not
the right approach.
Then, i would like to compute the elementary residual at each cell
<R(u),v>, that is to say compute
For each cell, {R(u)} = 2*a(grad v, grad u) - a(v,f) - [Kup][Kpp]^-1[Kpu]{u}
This formula does not make sense. The terms
a(grad v, grad u)
and
a(v,f)
are numbers (they are the result of integration) whereas
[Kup][Kpp]^-1[Kpu]{u}
is a vector. You cannot add numbers and vectors.
std::vector<double> weights(support_points.size(),1);
const Quadrature<dim> node_quadrature_formula(support_points,weights);
FEValues<dim> fe_node_values (fe, node_quadrature_formula,
date_values | update_gradients |
date_quadrature_points | update_JxW_values);
But then i will work with the type "std::vector<Tensor<1,dim>>" which is
difficult to handle with the "FullMatrix" of the extracted submatrix, as
i have to compute [Kpu]{u}.
You have a conceptual misunderstanding. The std::vector<Tensor<1,dim>>
are the vector-valued values of the velocity at the evaluation points.
But when you want to compute...
Then how can i compute [Kpu]{u} ?
...the {u} are the *nodal values* of the velocity. These are not the
same. It is not a problem of how these two things are represented in
data structures, but that they are conceptually different. You simply
cannot multiply [Kpu] by a collection of velocity vectors; [Kpu] needs
to be multiplied by a vector of nodal values.
Best
W.
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