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?
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.