At present ,I am doing the work about Discontinuous Galerkin methods.I viewed many papers,but I have many problems. For example: 1.How to understand the discontinous 2.choice of basis function 3.what the difference of the spectral element method and DG 4.whether the DGM can solove N-S equations

If somebody are interested in the DGM,Can you send me e-mail.Tks

1) The solution is discontinuous at the boundary of 2 neighbouring cells/elements. This is not so strange actually, you have the same with finite volume schemes. There you only have a cell average which also isn't the same for neigbouring volumes.

2) Lots of freedom to choose base functions, depends heavily on what kind of element (hex, tet, ...) and implementation. Nodal base functions based on orthogonal polynomials seem to have advantages.

3) There exist numerous definitions of spectral element method. Hard to answer this one without knowing what you mean by spectral element.

4) Yes, DGM can solve N-S.