[dune-pdelab] artifact in DiscreteGridfunctionGradient in parallel run

[Jö Fahlke]

Hi!

The reason for this behaviour is that you are using Q1 finite elements.  For
Q1 the gradients cannot be continuous across element boundaries.

So in each vertex the vtk-writer will use the gradient obtained in one of the
adjacent elements -- it just happens that yaspgrid is a structured grid
manager and which element's value ends up being used is not arbitrary.

Also this happens not only on the parallel boundary, but also on other domain
bounadiries -- it just so happens that it is very obvious on the parallel
boundary, and your choice of function to interpolate makes it very difficult
to see at the domain boundaries.  I've attached output from a function x*x+y*y
instead, which better shows the effect.

You can use the VTKWriters non-conforming mode to get a better visualization
of the finite element method's idea of what the gradients are.  Whether that
is good enough for further analysis however is another question.

Regards,
Jö.

Am Do,  1. Aug 2019, 18:06:08 +0200 schrieb Jö Fahlke:
> Here is the output produced by the program and a screenshot of the defect.  It
> shows the x-component of the gradient, which is perpendicular to the partition
> boundary.  Not that on right partition, the x-value of the gradient seem to
> have been copied from the first interior vertex to the closest border vertex.
> 
> Regards,
> Jö.
> 
> -- 
> Jorrit (Jö) Fahlke, Institute for Computational und Applied Mathematics,
> University of Münster, Orleans-Ring 10, D-48149 Münster
> Tel: +49 251 83 35146 Fax: +49 251 83 32729
> 
> Kiss a non-smoker; taste the difference.
> -- fortune


> <?xml version="1.0"?>
> <VTKFile type="PUnstructuredGrid" version="0.1" byte_order="LittleEndian">
>   <PUnstructuredGrid GhostLevel="0">
>     <PPointData Scalars="field" Vectors="gradient">
>       <PDataArray type="Float32" Name="field" NumberOfComponents="1"/>
>       <PDataArray type="Float32" Name="gradient" NumberOfComponents="3"/>
>     </PPointData>
>     <PCellData>
>     </PCellData>
>     <PPoints>
>       <PDataArray type="Float32" Name="Coordinates" NumberOfComponents="3"/>
>     </PPoints>
>     <Piece  Source="s0002-p0000-output-00000.vtu"/>
>     <Piece  Source="s0002-p0001-output-00000.vtu"/>
>   </PUnstructuredGrid>
> </VTKFile>






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-- 
Jorrit (Jö) Fahlke, Institute for Computational und Applied Mathematics,
University of Münster, Orleans-Ring 10, D-48149 Münster
Tel: +49 251 83 35146 Fax: +49 251 83 32729

featured product: Debian GNU/Linux - http://www.debian.org
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<?xml version="1.0"?>
<VTKFile type="PUnstructuredGrid" version="0.1" byte_order="LittleEndian">
  <PUnstructuredGrid GhostLevel="0">
    <PPointData Scalars="field" Vectors="gradient">
      <PDataArray type="Float32" Name="field" NumberOfComponents="1"/>
      <PDataArray type="Float32" Name="gradient" NumberOfComponents="3"/>
    </PPointData>
    <PCellData>
    </PCellData>
    <PPoints>
      <PDataArray type="Float32" Name="Coordinates" NumberOfComponents="3"/>
    </PPoints>
    <Piece  Source="s0002-p0000-output-00000.vtu"/>
    <Piece  Source="s0002-p0001-output-00000.vtu"/>
  </PUnstructuredGrid>
</VTKFile>
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