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October  2007, 8(3): 663-676. doi: 10.3934/dcdsb.2007.8.663

Error estimates for finite element approximations of consistent splitting schemes for incompressible flows

Jie Shen 1, and  Xiaofeng Yang 1,

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

Received  July 2006 Revised  March 2007 Published  July 2007

We study a finite element approximation for the consistent splitting scheme proposed in [11] for the time dependent Navier-Stokes equations. At each time step, we only need to solve a Poisson type equation for each component of the velocity and the pressure. We cast the finite element approximation in an abstract form using appropriately defined discrete differential operators, and derive optimal error estimates for both velocity and pressure under the inf-sup assumption.
Keywords: finite elements, consistent splitting, Navier-Stokes equations, incompressibility, error estimates..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Jie Shen, Xiaofeng Yang. Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 663-676. doi: 10.3934/dcdsb.2007.8.663
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