I wrote a number of 1D/2D FE and FD programs as a bachelor student, but the main problem I continually came into contact with was gradient shocks related to convection/diffusion problems in convection-dominated flows. From my limited research this seems to be an inherent problem in continuous Galerkin FE methods.
Now I'm interested in jumping into the DG FE world. I've been doing some reading on the various forms of DG available, but I'm not really sure where to start. I've read about hybrid CG/DG methods, various limiters, h/p adaptivity, etc. All of this is really interesting, but difficult to find a beginning to start with.
Is it worth just focusing on the first paper by Reed and Hill from '73? Is there a more recent paper/textbook/lecture notes that gives a decent intro into DG methods without any overly specific information for a particular application? I'm looking to start but don't know where..