Hello,
I have some trouble with the accuracy of the displacement gradient in
moving mesh situations. I have attached a minimal example to reproduce
my problem. It consists of a unit cube just like the reference
configuration of the HEX8 element and outputs the solution and the
displacement gradient at each gauss point.
Without setting the DOFs to the coordinates of the mesh, everything is
simple (./ex26-opt):
> 0 0, grad: [(0, 0, 0), (0, 0, 0), (0, 0, 0)]
> 0 0, solution: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> 0 1, grad: [(0, 0, 0), (0, 0, 0), (0, 0, 0)]
> 0 1, solution: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
When setting the DOFs with mesh_position_get() there are inaccuracies
(./ex26-opt --set):
> 0 0, grad: [(1, -1.38778e-17, -2.77556e-17), (0, 1, -2.77556e-17), (0,
> -4.16334e-17, 1)]
> 0 0, solution: -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1
>
> 0 1, grad: [(1, 1.04083e-17, 1.07553e-16), (0, 1, 3.1225e-17), (0,
> -1.04083e-17, 1)]
> 0 1, solution: -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1
>
Only when using TET4 instead of HEX8 elements I get the expected
results:
> 0 0, grad: [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
> 0 0, solution: -1 0 -1 0 -1 0 1 0 -1 -1 -1 0
> 0 1, grad: [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
> 0 1, solution: -1 0 -1 0 -1 0 1 0 -1 -1 -1 0
As these small errors accumulate, I would like to know if there is any
possiblity to get a gradient with a better accuracy with hex8 elements.
I am using libmesh 0.7.1 and used the following flags for compiling
libmesh:
$ ./configure --enable-mpi --enable-shared
--enable-unordered-containers --enable-periodic --enable-ghosted
--enable-second --enable-petsc --enable-slepc --enable-laspack
--enable-gzstreams --enable-bzip2 --enable-vtk --enable-tecplot
--enable-exodus
Robert
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