#TIL how Fourier transforms and #pseudospectral methods are intimately related to #FEM. What was missing from the picture is how a tool for numerical integration could be used for numerical differentiation.

If you think about it, Fourier transforms are also expressed as integration over an interval in space. When you differentiate a function it only affects the basis. For example:

exp(ikx) -> ik * exp(ikx)

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