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What are the main differences between finite element and finite difference approach for incompressible flow simulations? I have a vague idea about how FE methods rely on minimizing the residual over elements and FD methods consider Taylor series approximation of different terms in NS equations.

Based on my little experience, I have observed that most of the codes in fluid dynamics community are based on finite volume/finite difference methods rather than FE methods. Are there any subtle reasons regarding why FD/FV methods are much more prevalent than the FE methods in flow simulations?

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    $\begingroup$ "Classical" FE methods applied to NS equations require some form of stabilization and are generally non-conservative. For the most part, all the problems FE methods have been overcome with the development of methods for stabilization and the use of discontinuous elements. FV methods continue to be in use by the CFD community possibly due to their history. FV methods may also be more physically intuitive for fluid flow problems, and may be easier to teach to engineers. They may also be easier to implement. $\endgroup$
    – A. B. Marnie
    Commented Jun 28, 2018 at 17:56

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"Classical" FE methods applied to NS equations require some form of stabilization and are generally non-conservative. For the most part, all the problems FE methods have been overcome with the development of methods for stabilization and the use of discontinuous elements. FV methods continue to be in use by the CFD community possibly due to their history. FV methods may also be more physically intuitive for fluid flow problems and may be easier to teach to engineers. They may also be easier to implement.

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