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Can boundary layer theory be applied in finite element methods as it is applied in finite volume method? i.e The flow away from the boundary is considered inviscid and solved first, then the flow inside the boundary layer is solved?

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    $\begingroup$ I don't see why not, in principle. The FV method is really just a generalization of the FE method. What is often termed "the FE method" is just one simple version of the general idea. Finite elements don't have to have nice simple piecewise continuous low-order-polynomial shape functions. $\endgroup$ – alephzero Jan 28 '19 at 2:14
  • $\begingroup$ But i never see it being applied in finite element case. In FE, instead either the mesh is refined (h version) where the gradient is steep or the polynomial order of finite element is increased (p version). $\endgroup$ – EngDR Jan 28 '19 at 6:31
  • $\begingroup$ Well, now's you chance to publish some research, if it works well ;) $\endgroup$ – alephzero Jan 28 '19 at 17:41
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It can but you are wasting the full potential of the method when doing it so. I recommend you look into "Applied partial differential equations" by Trim. You can also check a few articles in perturbation theory which solves part of the boundary layer. Doing finite element is just useful when you are programming it.

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  • $\begingroup$ Unless there are more than one similar book and I'm looking at the wrong one, Trim doesn't even mention the OP's question. It may be a good book for the topics it does cover, but at a quick glance all the contents are at least 50 years old, and there are no references to research papers. $\endgroup$ – alephzero Jan 28 '19 at 17:40

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