On 10/22/19 10:41 AM, Xiang Sun wrote: > > In step-31, why did you define the residual by multiplying T^(a-1)? What does > "a" mean? Thank you very much.
I assume you mean here? https://dealii.org/developer/doxygen/deal.II/step_31.html#Stabilizationweakformandspacediscretizationforthetemperatureequation To understand the form stated there, you have to go back to the paper by Guermond and Popov. In essence, this goes back to some deep theory about hyperbolic equations that says that a weak solution is a physical solution only if it satisfies an entropy inequality. There are many ways to define an entropy pair (a pair of functions), and one of these is to choose E=T^a. The differential inequality E then has to satisfy is obtained by multiplying the equation for T by T^{a-1}. The theory is not particularly simple, and requires substantial background of hyperbolic equations. Going to the papers by Guermond and coauthors will give you the necessary insight. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: bange...@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. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/da53a1b5-6281-9389-9acd-a8a8747e76e8%40colostate.edu.
