The orientation of the normal vector on an inner interface

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1

Dear NGSolve developers,

I am not able to solve a transmission problem for the Laplace problem using the hybridized mixed method with static condensation. I wonder if the “element_boundary” method gives a normal vector with the same orientation from both sides of the interface.

Programming the same problem using the “skeleton” NGSolve style gives the right answer.

Best regards,
Salim

Attachment: Version_OK.py

Attachment: Version_WrongSolution.py

2

Hi Salim,

in an element-boundary integral, the normal vector is always pointing outside of the element.

The problem with your ‘wrong solution’ is that a discontinuous H(div) has no Trace anymore.

To build the right hand side with the jump1 - term, you can do element-boundary integrals everywhere, and multiply with a selection function set to 1 at the interface.

Joachim

3

Dear Joachim,

Thank you very much for the quick answer and for providing a solution to my problem.

Best,
Salim