# [deal.II] How to get normal / tangential vectors at nodes, not at quadrature points?

Hello Deal.II Users,


I am working on setting a constraint: (V - v_s ) \cdot n =  \phi_f (v_f -
v_s) \cdot n  on three vector variables at the interface with affine
constraint class in Deal.II's library.

(Where, V, v_s, and v_f are velocity vectors on two different domains,  and
they are coupled with each other at the interface; n is the normal vector;
\phi_f is the volume fraction.)

I decided to constrain either V_x= -(...) / n_x  or  V_y= -(...) / n_y
depending on the absolute values of n_x or n_y (n_x and n_y are the
components at x, y directions of the normal vector n).

Now, I have a problem with getting the normal vectors *at nodes *when
playing with affine constraint within the fe_nothing and hp:finite element
framework. The relevant function/class I have found in Deal.II's library
all return the normal vector *at quadrature points,* not at nodes.

Have you ever encountered a problem like this? Could you kindly share me
your idea of handling this problem? Thousand of thanks.

Best,

Lei Li

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• [deal.II] How to get normal / tangential vectors at nodes, no... Lex Lee