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I have to deal with FEM and the numerical solution of PDEs a lot. While I'm doing ok when just applying or implementing it, I observe a lack of understanding when authors begin to argue with "Ritz", "Galerkin", "Weak Form", "Integration by parts" and so on.

Can anyone recommend me a good book to get some basics in that field, specifically targeted to understand FEM and the numerical solution of PDEs.

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The book of Thomas J.R. Hughes : The finite Element Method, Linear static and dynamic finite element analysis, is probably the reference that you need.

You could find in the first chapter the building of the discretized form of a simple one-dimensional boundary-value problem from its strong formulation.

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  • $\begingroup$ This is indeed a good reference but it is very much oriented toward structural mechanics so I doubt it is what the OP is looking for. $\endgroup$ – Bill Greene Jul 3 '17 at 19:01

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