A Nonconforming Finite Element Method for the Stationary Navier--Stokes Equations
- 1 February 1998
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 35 (1) , 93-120
- https://doi.org/10.1137/s0036142996297199
Abstract
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.Keywords
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