Re: [Getfem-users] Quadrature question.

[Renard Yves]

Ronan Perrussel <address@hidden> a écrit :

> Dear getfem users,
>
> I am using getfem for solving an axisymmetric problem and I have to  
> integrate a term of the following form :
> \int_\Omega 1/r u v dr dz
> where u and v are respectively solution and test function, r is the  
> radial distance and z is the height.
> Of course u and v are enforced to be zero on the axis. Consequently  
> the integrand should be regular even for the elements touching the  
> axis.
> I wonder how to perform an accurate quadrature of this term  
> particularly for the elements touching the axis because I do not  
> know how to describe the function 1/r properly by a mesh_fem object  
> (only in the area close to the axis).
> I could do something by hand for the elements touching the axis but  
> it would be helpful if someone had a better proposition.
>
> Thanks in advance for your proposition(s).
> Best regards,
>
> Ronan

Dear Ronan,

If the integral is not singular, you can use a standard integration  
method (there is also some adpated integration methods for some  
singular terms in the Xfem implementation). You can represent the 1/r  
term with a mesh_fem_global_function object.

I hope this can help you.

Yves.