Abstract
In this paper, we propose and analyze a new artificial compressibility splitting methodwhich is issued from the recent vector penalty-projection method for the numerical solutionof unsteady incompressible viscous flows introduced in [1], [2] and [3].This method may be viewed as an hybrid two-step prediction-correction methodcombining an artificial compressibility method andan augmented Lagrangian method without inner iteration.The perturbed system can be viewed as a new approximation to the incompressible Navier-Stokes equations.In the main result,we establish the convergence of solutions to the weak solutions of the Navier-Stokes equationswhen the penalty parameter tends to zero.
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