DG introduction
I'm familiar with CG well (and FVM as well), but I do not have any knowledge about DG, can anyone suggest me a suitalbe an introductory reference (brief that gives concept)

Re: DG introduction
I like the sections on DG in Karniadakis & Sherwin `Spectral/hp element methods for CFD'. For elliptic problems, there are several inequivalent approaches with different stability, consistency, and computational properties. Arnold and others 2002 `Unified analysis of DG for elliptic problems' is a good start, but somewhat technical.

Re: DG introduction
B.Q. Li, 'Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer', Springer 2005

Re: DG introduction
John,
I have received lecture notes from Bernardo Cockburn (cockburn@math.umn.edu), one of the major players in this field. You may contact him directly, or else send me your email and I'll forward it to you. ami 
Re: DG introduction
please forward a copy to me (john.dongarra@gmail.com), thanks.

Re: DG introduction
Please find it in your mailbox.

Re: DG introduction
Thank, but what you sent to me is not a Lecture note, but is a review paper, which is not useful for starter!

Re: DG introduction
Well, this is what I had from him. As a last help I can offer, have a look at this ppt presentation: www.iacmm.org.il/ISCM20/DGM_ISCM20T.ppt
Hopefully, this will be helpful. 
Re: DG introduction
Thanks for your knid effort.

Re: DG introduction
You are welcome. If it does not serve your need, the cats pictures at least are cute...

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I've found the Book by Li not very good... why not try the Hesthaven book (has become standard in the field) or Kopriva's DGSEM? I find both of them to be much more readable as well

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For more and advanced information on modal DG method you can look the thesis of Landamann:
http://elib.unistuttgart.de/opus/vo...9/pdf/diss.pdf Also, if you want to understand very well the dg method you must read by books or papers the below matters: 1.Schemes of finite volumes theory (due to relation of dg with finite volumes (discontinuity at interfacesfluxes)) 2.Riemann solvers (mainly approximate Riemann solvers) 3.Spectral & high order Elements 
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I'd still recommend DG SEM by Kopriva for a beginner... Regarding the Riemann solvers: that depends on what you want to do with your code.... for wellresolved problems, the Riemann solvers shouldn't really matter at all, but for underresolved probs, I agree... Cheers! 
The choice of Riemann solver play important role for DG formulation. Is the way that an element derives information by neighbour elements.
Mainly for solutions with large gradients or discontinuities(such as shocks) the Riemann solver is crucial part due to the resolution of solution at these regions. 
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Sure, Riemann solver couple the system, but due to the higher polynomial approximation in the cells, jumps at interfaces tend to be much smaller than for FV... Thats why you can get away with using a cheaper Riemann solver than FV. In fact, as long as you are decently resolved, lax Friedrichs is ok most of the time! Regarding shock capturing: shocks on coarse grids are generally not captured at the grid cell interface, but within the cell!! And thats done by stabilizing with viscosity, not by the Riemann solver. So, as you see, in DG Riemann solvers play a less important role than in FV! Cheers! 
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