I am solving some 2nd order differential equations using the finite element method. Doing so I represent the second order derivative at a given point as:(adsbygoogle = window.adsbygoogle || []).push({});

∂^{2}ψ_{i}/∂x^{2}= 1/(Δx)^{2}(ψ_{i-1}+ψ_{i+1}-2ψ_{i})

And solve the differential equation by setting up a matrix of N entries and solving for the eigenvectors. I guess you are all familiar with this approach. Now what I want to do is use a nonuniform mesh. To do so I have tried to simply let Δx = Δx_{i}, i.e. such that it may vary depending on the site i. But doing so I get some solutions that don't make sense, which I assume is because of the "discontinuity" in the mesh size.

How can I approach the problem of a nonuniform mesh size?

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# Nonuniform finite element method

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