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

[Wen Jiang]

Dear Prof Yves Renard,

Thanks for your suggestions. However I still have some concerns about the accuracy of the interpolation.

Basically I would like to extract the displacement and strain field at the crack tip. At the crack tip the field is spanned by the sum of the standard basis function and enriched basis functions(like Heaviside and tip enrichment). I do not know how the accuracy would be if we first interpolate the gradient/Hessian of the original finite element on a discontinuous finite element with only standard shape function. I think that is the reason that previously I used interpolator_on_mesh_fem to get the gradient/Hessian because I guess that function uses the original finite elements for interpolation. Any suggestions?

Also I am not very clear about how to use the interpolation function in getfem_interpolation.h to interpolate on a cloud of points. Which function should I call exactly and how to define those points as the input of such function? Thanks.

Regards,
Wen

On Wed, Feb 12, 2014 at 6:53 AM, Yves Renard <address@hidden> wrote:

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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