A fully discrete stabilized finite-element method for the time-dependent Navier-Stokes problem

Author:
  • YHYinnian He
    Yinnian He
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Abstract
A fully discrete stabilized finite‐element method is presented for the two‐dimensional time‐dependent Navier–Stokes problem. The spatial discretization is based on a finite‐element space pair (Xh, Mh) for the approximation of the velocity and the pressure, constructed by using the Q1 – P0 quadrilateral element or the P1 – P0 triangular element; the time discretization is based on the Euler semi‐implicit scheme. It is shown that the proposed fully discrete stabilized finite‐element method results in the optimal order error bounds for the velocity and the pressure.