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Re: [Getfem-users] divergence of stress tensor

From: Huu Phuoc BUI
Subject: Re: [Getfem-users] divergence of stress tensor
Date: Fri, 19 Jan 2018 15:02:53 +0100

Dear Yves,

Thank you for your reply!

We expressed the divergence of stress tensor with respect to the variable u. In the _expression_, we have something like Grad(Trace(Grad_u)), and Trace(Hess_u). When assembling these terms with GetFEM, there is an error in assembly string. I tried to assembly separately these two terms. Both did not work.

For the first term Grad(Trace(Grad_u)), I think the error comes from the fact that, in GetFEM, we can only use Grad operator with a variable, i.e., Grad_u, Grad_Test_u, etc. Therefore, we can not write directly Grad(Trace(Grad_u)). Is it right?

For the second term Trace(Hess_u), I think the error comes from the Trace operator, since in the GetFEM documentation, it is stated that Trace operator is used for a square matrix. In our case, since u is a vector field, Hess_u is a tensor of order 3. Can we use Trace operator in assembly string for a tensor of order 3? 

Thank you in advance for your reply.

Best regards,


On Tue, Jan 16, 2018 at 5:32 PM, Yves Renard <address@hidden> wrote:

Dear Phuoc,

There is no specific function for that, but you have access to the Hessian ('Hess_u' for the variable u), so you have to give the _expression_ of the divergence of the stress tensor with respect to the Hessian of the variable.

Additionally, for the jumps on normal derivatives on element interfaces see

Best regards,


Le 16/01/2018 à 06:08, Huu Phuoc BUI a écrit :
Dear getfem users,

I'd like to compute the divergence of stress tensor of a linear elasticity problem which is necessary in an a posteriori error estimate.

Do you have any idea how to compute it using generic assembly of GetFEM? 

Thank you
​ in advance for your support.​

Best regards,


  Yves Renard (address@hidden)       tel : (33)
  Pole de Mathematiques, INSA-Lyon             fax : (33)
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE


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