Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

I extended the step-26 documentation and provided a pull request on github. You can create an iterator to the elements of a matrix row. Would that do > what > you need? > Yes, that's exactly what I was looking for. I just somehow missed the informa

Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

Yes, I will do that. I could either enhance the introduction, or write a new paragraph in the 'Possibilities for extensions' sections. I guess the latter option would be the better one. Either would be great! I could provide a code snippet on how to check for positivity preservation, but f

Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

Hi Wolfgang, On Monday, December 18, 2017 at 1:45:15 AM UTC+1, Wolfgang Bangerth wrote: > > I think your observation of negative values is an interesting one (and > surprising one, for many). Would you be interested in writing a couple of > paragraphs about time step choice for the introduction

Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

On 12/13/2017 09:06 AM, Marc Fehling wrote: 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

Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

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, prob

Re: [deal.II] Re: Heat equation (step-26): Negative values with small time step

Thomee shows that using small time steps can lose positivity in some schemes, see On Positivity Preservation in Some Finite Element Methods ... - Springer

[deal.II] Re: Heat equation (step-26): Negative values with small time step

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:

[deal.II] Re: Heat equation (step-26): Negative values with small time step

Marc, On Thursday, December 7, 2017 at 11:52:39 AM UTC-5, Marc Fehling wrote: > I stumbled over some interesting behavior of the heat equation from > step-26. If I reduce the time step to a smaller value, let's say to 1e-6, I > observe negative values for the solution near the sources (where gr