Re: [Getfem-users] second derivative of linear elements

[Yves Renard]

Dear Wen, 

interpolator_on_mesh_fem is a structure which mainly allows to use a 
precomputed solution to enrich a finite element space. It only interpolate the 
solution and its gradient. It is an interpolation, thus the gradient of a P1 
function will be constant over an element, yes. If you just need to interpolate 
a gradient or a Hessian on a cloud of points, you should preferably use the 
functions in getfem_derivatives.h and getfem_interpolation.h but you should 
first interpolate the gradient/Hessian on a discontinous finite element on the 
same mesh, then use the interpolation function in getfem_interpolation.h to 
interpolate on a cloud of points. Of course, it would be possible to provide a 
function which performs both the two operations in only one step, but it does 
not exist for the moment.

Best regards,

Yves.





----- Original Message -----
From: "Wen Jiang" <address@hidden>
To: address@hidden
Sent: Tuesday, February 11, 2014 11:41:55 PM
Subject: Re: [Getfem-users] second derivative of linear elements




Sorry to clog your inbox. In my previous email I forgot to tell that I used 
interpolator_on_mesh_fem to get the gradient and hessian. Basically I would 
like the get the first derivative and second derivative of the displacement 
field at some points. I understand that the gradient is definitely 
discontinuous across elements so we have to use a discontinuous fem as the 
targeted fem if the compute_gradient() is used. But I am not sure about how the 
gradient and hessian is calculated when calling 
interpolator_on_mesh_fem.eval(...) and .eval_hess(...). As I said, if the 
linear element is used, are those results still correct? Thanks. 

Regards, 
Wen 




On Tue, Feb 11, 2014 at 9:55 AM, Wen Jiang < address@hidden > wrote: 




Dear all, 

I tried to calculate the second derivative in getfem using compute hessian. For 
linear elements, the second derivative of the shape function should be zero but 
it seems that the results of hessian computed in getfem is not zero. Could you 
tell me how is the hessian computed in getfem for linear elements? Thanks. 

Regards, 
Wen 


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