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Asymptotic and numerical solutions to PDE not agreeing with each other

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I am trying to verify a leading-order asymptotic solution (as ) of the problem


I have determined that a composite solution to the problem, at leading-order, is

and I have checked that this satisfies the PDEs and boundary conditions, and they are all satisfied (and although the composite solution does not satisfy the boundary conditions at exactly, it does agree up to exponentially small corrections as .)

I am trying to solve this exact problem in COMSOL (with ), but the analytical solution and the solution obtained by COMSOL do not seem to be agreeing with each other, which is very odd. Although they show the same qualitative behaviour, I would hope that the solutions are close together numerically, and they are not (perhaps due to a scale factor gone awry somewhere).

I have attached screenshots of my implementation in COMSOL, and would like some clarification as to whether I have implemented the problem correctly, and whether there is something subtle (or not) that I have missed. I also include the COMSOL file for completeness.

0 Replies Last Post Jul 9, 2021, 8:37 a.m. EDT
COMSOL Moderator

Hello Oliver Bond

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