Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations

He, Yinnian

doi:10.1090/S0025-5718-05-01751-5

Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations
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Math. Comp. 74 (2005), 1201-1216 Request permission

Abstract:

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair $(X_h,M_h)$ which satisfies some approximate assumption. An optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters $\epsilon ,~\Delta t$ and $h$ are sufficiently small.

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