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Can anybody recommend me a good introduction to Crouzeix-Raviart Finite Elements? Their motivation is not obvious and the body of literature is hard to overlook.

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I'd take a look at Chapter 3 of the FEniCS book. They cover common and unusual finite elements

In short, a Crouziex-Raviart element is a non-conforming finite element used typically for $H^1$ or $C_0$ discretizations. The nonconformity comes from the fact that continuity is only enforced on a CR element's midpoint as opposed to vertices. For scalar $P_1$ Crouziex-Raviart elements, this reduces down to the condition that the average of the solution is continuous, i.e. over an element edge $e$, $\int_{e}[[u]] = 0$.

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