Hi,

I would like to know how many of you guys write DG codes for NS/RANS. Also, I see a lot of work has been done on DG, but it looks like nobody explored Discontinuous Finite Elements in general, where test and basis (shape) functions need not be the same. Is there any reason for this, apart from the difficulty of proving stability theorems?

Best Regards,

Sergio

A lot of work has been done with DGFEM framework. test function and basis function's different choice lead to different finit element method,if test function is identical to basis function ,it is called galerkin method...

What you were looking for is called a Petrov-Galerkin method which is widely used.

Hi, Jack,

have you got any references? Thanks,

Best regards,

deltaquattro

Hi, Jed,

I know the definition of Petrov-Galerkin method, thanks I was looking for specific references on Petrov-Galerkin methods in the field of DGFEM. Since DG with some numerical fluxes is nonlinearly stable for convection-diffusion equations, the main thrust to the use of Petrov-Galerkin methods seems to be lacking. However, it is strange that nobody tried it, anyway. So I was looking for references, ideally comparing classical DGFEM approach and general DFEM approach.

Best regards,

Sergio

So it sounds like you are interested in a Discontinuous Petrov-Galerkin method. This is the first of several papers by the same authors. I don't know of any comparative studies.

@article{bottasso2002dpg, title={{The discontinuous Petrov--Galerkin method for elliptic problems}}, author={Bottasso, C.L. and Micheletti, S. and Sacco, R.}, journal={Computer Methods in Applied Mechanics and Engineering}, volume={191}, number={31}, pages={3391--3409}, year={2002}, publisher={Elsevier} }

Thank you very much, Jed, that´s what I was looking for.

Best,

deltaquattro