2d advection-diffusion: cell Péclet number and numerical stability - Computational Science Stack Exchange most recent 30 from scicomp.stackexchange.com 2022-01-27T03:29:51Z https://scicomp.stackexchange.com/feeds/question/40028 https://creativecommons.org/licenses/by-sa/4.0/rdf https://scicomp.stackexchange.com/q/40028 2 2d advection-diffusion: cell Péclet number and numerical stability Max_89 https://scicomp.stackexchange.com/users/38094 2021-09-07T17:06:24Z 2021-09-07T19:16:50Z <p>I am studying the numerical resolution of 2d advection-diffusion problems with finite element methods.</p> <p><span class="math-container">$$\frac{\partial u}{\partial t} + \beta\cdot\nabla u = \nabla\cdot(\nabla u) \, .$$</span></p> <p>It is said in <a href="https://uk.comsol.com/blogs/understanding-stabilization-methods/" rel="nofollow noreferrer">this article</a> on the COMSOL blog that it has been mathematically proven that the condition on the cell Péclet number</p> <p><span class="math-container">$$\mathrm{Pe}:= \frac{\Vert \beta\Vert h}{2c} &gt; 1\, ,$$</span></p> <p>leads to numerical instabilities.</p> <p>Could you please point me to any reference rigorously justifying such a statement?</p>