Hi Doug, Sorry for the late reply, I haven't checked convergence rigorously. I've just been checking by eye to see if the solution diverges or not, and have seen that the advection does better than diffusion. I'll do some more rigorous error analysis this week probably and let you know if I get better convergence. As for my implementation, I've just taken the upwind DG scheme from tutorial step-12 and added the time evolution by adding a mass matrix and solving the implicit backwards Euler time discritization.
Best, Gary On Fri, 26 Apr 2019 at 14:12, Wolfgang Bangerth <[email protected]> wrote: > On 4/26/19 9:48 AM, Gary Uppal wrote: > > > > Thanks for the reply. I get problems on less distorted meshes as well. > > For example, in the mesh with a hole shown below. I eventually need > > multiple holes and an advection term. Actually, the advection seems ok > > and I mainly get issues when the diffusion is large. If the distorted > > mesh is the issue, is there a better way to construct the geometry? > > No, your mesh is reasonable. The question is not whether the error is > large on cells that are not squares (it may be -- the finite element > theory doesn't ever guarantee that the error is *small* on any given > cell of any given mesh), but whether you get the *correct convergence > order*. So looking at the solution on a single mesh is not a useful > strategy -- the question is how the error decays as you refine the mesh. > > 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 a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/ZSHIDbp7yfE/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > For more options, visit https://groups.google.com/d/optout. > -- 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]. For more options, visit https://groups.google.com/d/optout.
