A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations

Approximations to solutions of the inhomogeneous boundary value problem for the Navier--Stokes equations are constructed via a nonstandard finite element method. The velocity field is approximated using piecewise solenoidal functions that are totally discontinuous across interelement boundaries but which are pointwise divergence free on each element. The pressure is approximated by C0 functions. Optimal rates of convergence results are obtained requiring only local quasi-uniformity assumptions on the meshes.

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