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I have been studying some pertubation theory lately which i found very useful.

I then started thinking about how to approximate solutions to a 2d boundary value problem if the difficulty lies in the geometry of the boundary(I.e. not rectangular), and not in the diff. equation itself(i.e. the diff. equation has a closed form analytical solution for a rectangular domain).

Does anyone have thoughts on how to approximate such solutions if the domain is close to being rectangular?

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# Approximating solutions on non-rectangular domains

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