A two-level iterative method with Newton-type linearization for the stationary micropolar fluid equations. (English) Zbl 07899584
Summary: In this paper, a two-level Newton iterative method is proposed for the stationary micropolar fluid equations. Firstly, the original equations are solved on a coarse grid based on Newton-type linearization. Then, the simplified linearized equations are solved on a fine grid. The stability and error estimates of the method are given in the theoretical part. The results of the theoretical analysis show that when the coarse mesh size \(\boldsymbol{H}\) and fine mesh size \(\boldsymbol{h}\) satisfy the relation \(\boldsymbol{h=O(H^2})\), the two-level Newton iterative method can achieve an optimal convergence rate. Finally, the effectiveness and applicability of the method are verified by some numerical experiments.
MSC:
| 65-XX | Numerical analysis |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
Keywords:
two-level method; Newton iterative method; micropolar fluid equations; finite element method; error estimatesSoftware:
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