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

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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

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

Received July 2006 Revised March 2007 Published July 2007

Abstract
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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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