The scheme you wrote looks fine. If a=1, then you should get q=0 or something close to machine zero. What are you getting ? Here you are projecting the gradient onto a discontinuous polynomial space. The blowup probably happens when you solve your advection equation, and maybe you need to look there more carefully.
best praveen > On 20 Jul 2024, at 12:27 AM, Sean Johnson <sljohnso...@gmail.com> wrote: > > 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: bang...@colostate.edu <> >> 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 dealii+unsubscr...@googlegroups.com > <mailto:dealii+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/8515c6a2-dfa6-4742-9269-f199200eb1e1n%40googlegroups.com > > <https://groups.google.com/d/msgid/dealii/8515c6a2-dfa6-4742-9269-f199200eb1e1n%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/9830640D-F3A2-480E-A5F4-90AEE5863995%40gmail.com.
