Abstract
In this paper, we combine a stabilized nonconforming finite element method with a two-level method to solve the stationary Navier-Stokes equations. Numerical results are presented to show the convergence performance of this combined algorithm.
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Chen, Z.: Finite Element Methods and Their Applications. Springer, Heidelberg (2005)
Douglas Jr., J., Santos, J.E., Sheen, D., Ye, X.: Nonconforming Galenkin methods based on quadrilateral elements for second order elliptic problems. Math. Modelling and Numerical Analysis 33, 747–770 (1999)
Cai, Z., Douglas Jr., J., Ye, X.: A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations. Calcolo (36), 215–232 (1999)
Kim, Y., Lee, S.: Stable nonconforming quadrilateral finite elements for the Stokes problem. Applied Mathematics and Computation 115, 101–112 (2000)
Li, J., Chen, Z.: A new local stabilized nonconforming finite element method for the Stokes equations. Computing (82), 157–170 (2008)
Zhu, L., Li, J., Chen, Z.: A new local stabilized nonconforming fintite element method for the stationary Navier-Stokes equations (submitted for publication)
Xu, J.: A novel two-grid method for semilinear elliptic equatios. SIAM J. Sci. Comput. 15, 231–237 (1994)
Xu, J.: Two-grid finite element discritizations for nonlinear PDEs. SIAM J. Numer. Anal. 33, 1759–1777 (1996)
Layton, W.: A two-level discretization method for the Navier-Stokes equations. Comput. Math. Appl. 26, 33–38 (1993)
Layton, W., Lenferink, W.: Two-level Picard and modified Picard methods for the Navier-Stokes equatios. Appl. Math. Comput. 69, 263–274 (1995)
Layton, W., Tobiska, L.: A two-level method with backtracking for the Navier-Stokes equations. SIAM J. Numer. Anal. 35, 2035–2054 (1998)
Girault, V., Lions, J.L.: Two-grid finite element scheme for the transient Navier-Stokes problem. Math. Model. and Numer. Anal. 35, 945–980 (2001)
He, Y., Li, J., Yang, X.: Two-level penalized finite element methods for the stationary Navier-Stokes equations. Intern. J. Inform. System Sciences 2, 1–16 (2006)
Olshanskii, M.A.: Two-level method and some a priori estimates in unsteady Navier-Stokes calculations. J. Comp. Appl. Math. 104, 173–191 (1999)
He, Y.: Two-level method based on finite element and Crank-Nicolson extrapolation for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. 41, 1263–1285 (2003)
He, Y.: A two-level finite Element Galerkin method for the nonstationary Navier-Stokes Equations, I: Spatial discretization. J. Comput. Math. 22, 21–32 (2004)
He, Y., Miao, H., Ren, C.: A two-level finite Element Galerkin method for the nonstationary Navier-Stokes equations, II: Time discretization. J. Comput. Math. 22, 33–54 (2004)
He, Y., Liu, K.M.: Multi-level spectral Galerkin method for the Navier-Stokes equations I: time discretization. Adv in Comp. Math. 25, 403–433 (2006)
He, Y., Liu, K.M., Sun, W.W.: Multi-level spectral Galerkin method for the Navier-Stokes equations I: Spatial discretization. Numer. Math. 101, 501–522 (2005)
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Zhu, L., Chen, Z. (2010). A Two-Level Stabilized Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_81
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DOI: https://doi.org/10.1007/978-3-642-11842-5_81
Publisher Name: Springer, Berlin, Heidelberg
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