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Would you know what is the condition for stability for the advection-diffusion equation where we treat the diffusion part using Crank-Nicholson and the advection part using FCTS (forward in time centered in space)? I am applying von Neumann analysis but I am not sure about the final condition for stability. Do you know where I could find the proof for the stability of that scheme? Thank you

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  • $\begingroup$ The relevant question is whether you are in the advection or diffusion dominated regime. Can you tell more about which effect is dominant in your case? $\endgroup$ – Wolfgang Bangerth Jun 4 '14 at 12:58
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    $\begingroup$ You could try a splitting scheme where you solve the diffusion term implicitly, and then solve the advection term explicitly $\endgroup$ – James Jun 4 '14 at 13:46
  • $\begingroup$ Click in the advection-diffusion tag in this site. There a few examples of how to do this within the Crank-Nicolson framework. $\endgroup$ – boyfarrell Jun 5 '14 at 13:22
  • $\begingroup$ For example, this one, scicomp.stackexchange.com/questions/7399/… $\endgroup$ – boyfarrell Jun 6 '14 at 5:45

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