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I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.

First of all, I use the Control Volume method for discretization and they use Finite Element.

Second, they talk about variational forms and H and Q spaces \Omega domains, which I have seen for the first time.

Can anybody point my way to a document, or book, or small chapter where I can understand the mathematical variational point of view of the Navier Stokes equation as simple as possible? (I'm interested in the incompressible stationary case for a fluid, so, very simple.)

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  • $\begingroup$ Related physics.stackexchange.com/q/71257/25301; not entirely sure about the details of the recommended text(s) containing such chapters, however. It may be useful for you to check out at least the table of contents to see how useful it'd be. $\endgroup$ – Kyle Kanos Feb 18 '19 at 16:26
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I found two books which look interesting but still feel it is not "for dummies" enough.

  • The Finite Element Method: Theory, Implementation, and Applications, Texts in Computational Science and Engineering, by M. G. Larson and F. Bengzon

  • A Mathematical Introduction to Fluid Mechanics by Chorin and Marsden

But still if someone has a better suggestion for a variational Navier Stokes derivation that is not so mathematical for a physicist to understand, please let me know.

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I'm a physics undergrad student. I've been to self-studying continuum mechanics, and as a part of that reading some fluid dynamics stuff. At first I faced similar difficulties. Kip S Thorne's Modern Classical Physics helped me to grasp the physical intuition behind most of the concepts. Then I was motivated to study the variational formulation of fluid. It uses physicist's familiar language.

  • Badin, Gualtiero, Crisciani, Fulvio; Variational Formulation of Fluid and Geophysical Fluid Dynamics: Mechanics, Symmetries and Conservation Laws
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