### Question regarding derivation of weak form in undocumented DG Poisson demo

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Dear all,

I have studied and read this question and this demo. However, I have trouble understanding this term

Thank you very much!

Meen

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!

Meen

Community: FEniCS Project

### 1 Answer

3

The three terms with

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.

` 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

1

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.

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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