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I am learning about Disconinuous Galerkin methods. I fail to understand how he basis funcions are constructed. I understand that typically Legendre polynomial are used, but I can't see how they relate to the nodes.

In Continuous Galerkin methods, the basis funcions for a linear triangle (3 nodes) are:

$N_1(\xi, \eta) = 1 - \xi - \eta\\ N_2(\xi, \eta) = \xi\\ N_3(\xi, \eta) = \eta\\$

What are the basis functions for a linear triangle used in Discontinuous Galerkin methods? Say we choose Legendre polynomials of order 2, then I would have one basis function of order 0, one of order 1, and one of order 2 for each node?

mfnx
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  • There is nothing stopping you using those basis functions in DG - you will just be considering a broken Sobolev space. By this we simply mean that each triangle is independent of each other. – K-Q Mar 25 '21 at 15:51
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    I forgot about this question. I figured that out already (got my DG up and running). @K-Q you could write your comment as an answer. – mfnx Mar 25 '21 at 17:51

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It is good to hear you figured out your problem!

My response to your questions is thus. There is nothing stopping you using those basis functions in DG - you will just be considering a broken Sobolev space. By this we simply mean that each triangle is independent of each other.

K-Q
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