Stability of time-splitting schemes for the Stokes problem with stabilizedfinite elements

The time-dependent Stokes problem is solved using continuous, piecewise lin ear finite elements and a classical stabilization procedure. Four order-one methods are proposed for the time discretization. The first one is nothing but the Euler backward scheme and requires a large linear system involving the velocity and pressure unknowns to be solved. The other three schemes a llow velocity and pressure computations to be decoupled, namely the pressur e-matrix method, a method based on an inexact LU factorization, and an oper ator splitting method. Stability and condition number estimates are derived . Numerical experiments in two space dimensions confirm the theoretical pre dictions. (C) 2001 John Wiley & Sons, Inc.