Hi Praveen, thank you for your hint! Indeed, choosing a time step size according to the *threshold of positivity* from Theorem 6 of Thomée's paper will lead to nonnegative results.
However, choosing a step size slightly below this lower bound still yields the desired nonnegative results, probably because the system matrix is not a Stieltjes matrix, as I checked the entries of the stiffness matrix. But this more restrictive condition certainly puts you on the safe side. Best, Marc On Monday, December 11, 2017 at 6:06:00 PM UTC+1, Praveen C wrote: > > Thomee shows that using small time steps can lose positivity in some > schemes, see > > On Positivity Preservation in Some Finite Element Methods ... - Springer > <https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwiLu9_rt4LYAhUGPY8KHVmUAw4QFggmMAA&url=http%3A%2F%2Fwww.springer.com%2Fcda%2Fcontent%2Fdocument%2Fcda_downloaddocument%2F9783319155845-c2.pdf%3FSGWID%3D0-0-45-1493845-p177252909&usg=AOvVaw1fgCFhiiT7cBPAjTHhCE1m> > > Best > praveen > > On 11-Dec-2017, at 8:51 PM, Marc Fehling <[email protected] > <javascript:>> wrote: > > Hi Bruno, > > I only heard about applying flux limiters on advection/convection > problems, but not on diffusion-related ones. This conforms with what I > recently found in literature, but I may skipped something crucial. > > The equation of interest is the heat equation: > > > <https://latex.codecogs.com/gif.download?%5Cpartial_t%20u%20-%20%5Cpartial_x%28%20k%20%5Cpartial_x%20u%20%29%20%3D%200> > Do you think that flux limiters or TVDs work for a combination like this? > > > <https://latex.codecogs.com/gif.download?%5Cpartial_t%20u%20+%20%5Cpartial_x%28%20f%28u%29%20%29%20%3D%200%20%5Cquad%5Ctext%7Bwith%7D%5Cquad%20f%28u%29%20%3D%20-%20k%20%5Cpartial_x%20u> > I also suspect that I missed some lower bound on a stability constraint > for the factor (k*timestepsize)? But from von Neumann analysis, I only get > an upper one on that. > > I hope that one of you has any experience on that to share :) > > Best, > Marc > > -- > 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] <javascript:>. > 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.
