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## Re: [Getfem-users] elastostatic example error evaluation

 From: Yves Renard Subject: Re: [Getfem-users] elastostatic example error evaluation Date: Sat, 2 Nov 2013 09:06:09 +0100 (CET)

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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 -----
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.

Regards,
Wen

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