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Numerical Solution of the Navier-Stokes Equations by the Finite Element Method

Solving the Navier-Stokes equations using the finite element method is of great interest, as this method can be used in particular when these equations are defined in complex domains. However, explaining this method is far from straightforward, and in this article we have sought above all to provide the reader with clarification on the use of this method, without necessarily going into all the theoretical details, which are relatively complex to assimilate. In particular, we haven't gone into the questions of existence and uniqueness of solutions, which are nevertheless important issues for this type of problem, where some problems are open-ended. Likewise, for the sake of precision, we have confined ourselves to giving a few results on error majorization. For further details on the previous two questions, we refer the reader to the list of references, some of which require a good level...