DG Method for Mixed Formulations

#1

Hello everyone,

I need some basic explanations for the usage of DG elements. In some problems such as in demo:

https://fenics.readthedocs.io/projects/dolfin/en/2017.2.0/demos/mixed-poisson/python/demo_mixed-poisson.py.html

It uses DG with 0 degree, and does not use any jump or average terms. But in many examples in the literature includes the jump and average terms in variational formulations. Can anyone explain when the jump and average terms are required and when they are not required ? What would be wrong in the results if we do not use these jump and average terms ? Thanks. And it would be perfect if you could share a theory reference for DG.

#2

A good theory reference for DG applied to elliptic problems is this paper:

http://www-users.math.umn.edu/~arnold/papers/dgerr.pdf

Note that in the example you linked, the space for \tau and \sigma is H(\text{div})-conforming, i.e., normal components of these functions are continuous across interior facets. If you apply the DG machinery from the linked reference with this choice of spaces and the numerical fluxes are consistent and conservative (in the sense defined by the reference), the jump and average terms will be zero.

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#3

Hi kamensky,
Perfect, thanks a lot for the document also.