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

Brilliant! Thanks a lot. -Lei Li

On Friday, June 5, 2020 at 4:49:56 AM UTC-7, Simon Sticko wrote:
>
> Hi,
> I suspect that the condition you have would be easier to enforce weakly by
> adding terms to the weak formulation, as is done in e.g. discontinuous
> Galerkin.
>
> Nevertheless, if you still want the normals at the nodes you can create a
> "dummy" quadrature which has the nodes on the face as quadrature points:
>
> const FiniteElement<dim> &fe = ... // some element
>
>
> You can then use this quadrature in FEFaceValues to get the normals. Here,
> the weights of the dummy quadrature are inf, but if the normals are
> everything you need that isn't a problem.
>
> Best,
> Simon
>
> On Thursday, June 4, 2020 at 8:09:08 PM UTC+2, Lex Lee wrote:
>>
>> 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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