Question regarding derivation of weak form in undocumented DG Poisson demo

25 days ago by
Dear all,

I have studied and read this question and this demo. However, I have trouble understanding this term 
- dot(v*n, grad(u))*ds(1)
 From my understanding; this term should represent the Neumann boundary, not Dirichlet boundary. It would be great if someone can explain this T_T.

Thank you very much!

Community: FEniCS Project

1 Answer

25 days ago by
The three terms with ds(1) come from the penalty descretization of the laplacian (Jump and average are usually defined on the outer boundary facets as the value of the funtion on this facet). They also appear for the interior facets with dS correspondingly.
However, if you have homogenious Dirichlet conditions these terms vanish, which is not the case here, so you need to add them on the outer boundary as well.

You might want to read up on different DG penalty discretizations of the Laplacian.
Thank you very much! Do you have any recommended papers or books that I can take a look?
written 25 days ago by Teeratorn Kadeethum  
That depends probably where you are coming from. I am a mathematician, so I like the book "Mathematical Aspects of Discontinuous Galerkin Methods" by Di Pietro and Ern.

If you are an engineer there might be more suitable books for you.
written 25 days ago by Lukas O.  
Thank you very much!
written 25 days ago by Teeratorn Kadeethum  
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