Thanks again for your time I really do appreciate it and don't want to waste it. The added equation, although it is an advection equaiont, it is actually representing a diffusion term in the hyperbolic equation. Its just an intermediate term needed for local discontinuous galerkin. Using averages should be stable again based off of the textbook I am using. It is not optimized but it is simpler than doing alternate winding which is the optimized way and to minimize the chance of bugs I am just starting with the simplest form.
I will try and read some papers on stabilizing the method. Thanks! On Friday, July 19, 2024 at 3:16:30 PM UTC-6 Wolfgang Bangerth wrote: > On 7/19/24 14:37, Sean Johnson wrote: > > > > Would an equation so simple need stabilizing? > > Yes. It's an advection equation with no diffusion. There needs to be some > kind > of stabilization. At the very least you will have to use an upwind flux > somewhere. > > Best > W> > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/8515c6a2-dfa6-4742-9269-f199200eb1e1n%40googlegroups.com.
