Re: [Getfem-users] elastostatic example error evaluation

[Yves Renard]

Dear Wen,

You are right that from a purely mathematical view, there is a bias estimating 
the error as it is done in  elastostatic example. However, most of the time, 
the two errors are of the same order. For the moment, there is only one way to 
compute the error by accounting of the value of the exact solution in each 
Gauss point. This way is to use a mesh_fem_global_function  defined in 
getfem_mesh_fem_global_function.h. It defines a mesh_fem structure having a 
certain number of degrees of freedom globally defined on the mesh and 
represented by some global functions which will be interpolated on each Gauss 
point. It is used for instance in crack.cc and in particular allows to estimate 
the error with the exact solution. I also plane to accept user defined function 
directly in generic assembly but it is still a work in progress.

Yves.




----- Original Message -----
From: "Wen Jiang" <address@hidden>
To: address@hidden
Sent: Friday, November 1, 2013 4:34:26 PM
Subject: [Getfem-users] elastostatic example error evaluation






Hi, 

I am testing the elastostatic example in the test folder. I have a question 
about the error evaluation (L2 and H1). The way how the error is evaluated in 
the code is firstly to get the error only at the node and then to interpolate 
the node error and assemble. I do not think this is the general way that the 
error should be evaluated since the exact solution cannot be interpolated by 
the shape function for general cases. In the code, the l2 and h1 errors are 
just machine error when only 1by1 element is used. And this is because the 
error at the node is zero and the error interpolated within element is 
identical zero. 

Thus, I am wondering whether getfem++ provide any other method to calculate the 
errors in a better way, meaning that the exact solution is evaluated at each 
gaussian point instead of interpolating by the node value. 


Also I would like to know that whether the energy norm for elasticity problem 
has been implemented yet. 



Thanks in advance. 


Regards, 
Wen 

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