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I have been looking for stability analysis of general reaction-diffusion problems, of the form

$\frac{\partial u}{\partial t}=\nabla\cdot D\nabla u-k\,u$ ,

to be solved using the standard Finite Element in 2D with an explicit Euler time stepping. I haven't found any estimate or proof for the stability criteria for $\Delta t$ for this case, most of the literature seems to point to the solution of the Heat equation by Finite Differences in 1D.

I would like to know if someone can point me how to find the stability criterion in this case, especially for quadrilateral elements.

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  • $\begingroup$ What's your time stepping scheme? $\endgroup$ – Wolfgang Bangerth Jun 18 '15 at 2:05
  • $\begingroup$ The standard explicit Euler time stepping. $\endgroup$ – Robert Sep 20 '15 at 16:18
  • $\begingroup$ The reaction term adds no complications since its eigenvalues are all proportional to $k$. What matters is the largest eigenvalue, which increases with the mesh resolution, and this largest eigenvalue is only determined by the diffusion term. $\endgroup$ – Wolfgang Bangerth Sep 22 '15 at 21:59

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