Numerical analysis of the Crank-Nicolson extrapolation time discrete scheme for magnetohydrodynamics flows
作者： Yuhong Zhang , Yanren Hou , Li Shan
DOI: 10.1002/NUM.21989
关键词:
摘要: In this article, we consider the time-discrete method for three-dimensional incompressible magnetohydrodynamics (MHD) equations. The Crank–Nicolson extrapolation scheme is used time discretization. From previous articles, under assumption that solution has high regularity which cannot be realistically assumed, convergence of optimal two-order. modest assumptions initial values and body force, prove some new results MHD addition, derive unconditional our scheme, but convergent order not optimal. Furthermore, provide another conditional estimation to increase order. It shown rate half in H 1 -norm, at least a quarter increased L 2 -norm than uncondtional results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2169–2208,
sci-hub.se 参考文章(18)
Roger Temam, Navier-Stokes Equations and Nonlinear Functional Analysis ,(1987)
Max D. Gunzburger, Amnon J. Meir, Janet S. Peterson, On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics Mathematics of Computation. ,vol. 56, pp. 523- 563 ,(1991) , 10.1090/S0025-5718-1991-1066834-0
Yinnian He, The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data Mathematics of Computation. ,vol. 77, pp. 2097- 2124 ,(2008) , 10.1090/S0025-5718-08-02127-3
Cătălin-George Lefter, None, Feedback Stabilization of Magnetohydrodynamic Equations Siam Journal on Control and Optimization. ,vol. 49, pp. 963- 983 ,(2011) , 10.1137/070697124
Adrian T Hill, Endre Süli, Approximation of the global attractor for the incompressible Navier–Stokes equations Ima Journal of Numerical Analysis. ,vol. 20, pp. 633- 667 ,(2000) , 10.1093/IMANUM/20.4.633
Yinnian He, Weiwei Sun, Stabilized finite element method based on the Crank–Nicolson extrapolation scheme for the time-dependent Navier–Stokes equations Mathematics of Computation. ,vol. 76, pp. 115- 136 ,(2007) , 10.1090/S0025-5718-06-01886-2
Li Shan, Yanren Hou, Haibiao Zheng, Variational multiscale method based on the Crank–Nicolson extrapolation scheme for the non-stationary Navier–Stokes equations International Journal of Computer Mathematics. ,vol. 89, pp. 2198- 2223 ,(2012) , 10.1080/00207160.2012.704023
Vidar Thom{ée, Negative norm estimates and superconvergence in Galerkin methods for parabolic problems Mathematics of Computation. ,vol. 34, pp. 93- 113 ,(1980) , 10.1090/S0025-5718-1980-0551292-5
Yinnian He, Two-Level Method Based on Finite Element and Crank--Nicolson Extrapolation for the Time-Dependent Navier--Stokes Equations SIAM Journal on Numerical Analysis. ,vol. 41, pp. 1263- 1285 ,(2003) , 10.1137/S0036142901385659
Y. He, Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations Ima Journal of Numerical Analysis. ,vol. 35, pp. 767- 801 ,(2015) , 10.1093/IMANUM/DRU015