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The analysis of unsteady incompressible flows by a three-step finite element method. (English) Zbl 0772.76036

This paper describes a three-step finite element method and its applications to unsteady incompressible fluid flows. Stability analysis of the one-dimensional pure convection equation shows that this method has third-order accuracy and an extended numerical stability domain in comparison with the Lax-Wendroff finite element method. The method is cost-effective for incompressible flows because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor-Galerkin method, the present method does not contain any new higher-order derivatives, which makes it suitable for solving nonlinear multidimensional problems and flows with complicated boundary conditions.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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