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Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. (English) Zbl 1435.65119

Summary: The velocity correction method has shown to be an effective approach for solving incompressible Navier-Stokes equations. It does not require the initial pressure and the inf-sup condition may not be needed. However, stability and convergence analyses have not been established for the nonlinear case. The challenge arises from the splitting associated with the nonlinear term and rotational term. In this paper, we carry out stability and convergence analysis of the first-order method in the nonlinear case. Our technique is a new Gauge-Uzawa formulation, which brings forth a telescoping symmetry into the rotational form. We also provide a stability proof for the second-order method in the linear case. Numerical results are provided for both first- and second-order methods.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76U05 General theory of rotating fluids
35Q30 Navier-Stokes equations
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