[1] Bernardi, C. and Raugel, G. A conforming finite element method for the time-dependent NavierStokes equations. SIAM Journal on Numerical Analysis, 22, 455-473(1985)
[2] He, Y. N. Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations. Mathematics of Computation, 74, 1201-1216(2005)
[3] John, V. and Kaya, S. A finite element variational multiscale method for the Navier-Stokes equations. SIAM Journal on Scientific Computing, 26, 1485-1503(2005)
[4] Li, J., He, Y. N., and Chen, Z. X. A new stabilized finite element method for the transient Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 197, 22-35(2007)
[5] He, Y. N. and Sun, W. W. Stabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations. Mathematics of Computation, 76, 115-136(2007)
[6] Shan, L. and Hou, Y. R. A fully discrete stabilized finite element method for the time-dependent Navier-Stokes equations. Applied Mathematics and Computation, 215, 85-99(2009)
[7] Chen, G., Feng, M. F., and He, Y. N. Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations. Applied Mathematics and Mechanics (English Edition), 34, 1083-1096(2013) DOI 10.1007/s10483-013-1729-x
[8] Crouzeix, M. and Raviart, P. A. Conforming and nonconforming finite element methods for solving the stationary Stokes equations I. Analyse Num rique, 7, 33-75(1973)
[9] Shi, D. Y. and Wang, H. M. The Crouzeix-Raviart type nonconforming finite element method for the nonstationary Navier-Stokes equations on anisotropic meshes. Acta Mathematicae Applicatae Sinica, 30, 145-156(2014)
[10] Ye, X. Superconvergence of nonconforming finite element method for the Stokes equations. Numerical Methods for Partial Differential Equations, 18, 143-154(2002)
[11] Shi, D. Y. and Pei, L. F. Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L2 projection method. Applied Mathematics and Mechanics (English Edition), 34, 861-874(2013) DOI 10.1007/s10483-013-1713-x
[12] Wang, X. S. and Ye, X. Superconvergence analysis for the Navier-Stokes equations. Applied Numerical Mathematics, 41, 515-527(2002)
[13] Liu, H. P. and Yan, N. N. Superconvergence analysis of the nonconforming quadrilateral linearconstant scheme for Stokes equations. Advances in Computational Mathematics, 29, 375-392(2008)
[14] Shi, D. Y. and Yu, Z. Y. Superclose and superconvergence analysis of a low order nonconforming mixed finite element method for stationary Stokes equations with damping (in Chinese). Acta Mathematica Scientia, 33A, 735-745(2013)
[15] Ciarlet, P. G. The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978)
[16] Girault, V. and Raviart, P. A. Finite Element Method for Navier-Stokes Equations:Theory Algorithms, Springer-Verlag, Berlin/Heidelberg (1987)
[17] Heywood, J. G. and Rannacher, R. Finite element approximation of the nonstationary NavierStokes problem I:regularity of solutions and second-order error estimates for spatial disretization. SIAM Journal on Numerical Analysis, 19, 275-311(1982)
[18] Rannacher, R. and Turek, S. Simple nonconforming quadrilateral Stokes element. Numerical Methods for Partial Differential Equations, 8, 97-111(1992)
[19] Ming, P. B. Nonconforming Element vs Locking Problem (in Chinese), Ph. D. dissertation, Chinese Academy of Sciences, Beijing (1999)
[20] Xu, X. J. On the accuracy of nonconforming quadrilateral Q1 element approximation of NavierStokes problem. SIAM Journal on Numerical Analysis, 38, 17-39(2000)
[21] Hu, J., Man, H. Y., and Shi, Z. C. Constrained nonconforming rotated Q1 element for Stokes flow and planar elasticity (in Chinese). Mathematica Numerica Sinica, 27, 311-324(2005)
[22] Shi, D. Y., Ren, J. C., and Gong, W. A new nonconforming mixed finite element scheme for the stationary Navier-Stokes equations. Acta Mathematica Scientia, 31B, 367-382(2011)
[23] Shi, D. Y and Ren, J. C. Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes. Nonlinear Analysis:Theory, Methods and Applications, 71, 3842-3852(2009)
[24] Lu, X. L. and Lin, P. Error estimate of the P1 nonconforming finite element method for the penalized unsteady Navier-Stokes equations. Numerische Mathematik, 115, 261-287(2010)
[25] Wang, J. L., Si, Z. Y., and Sun, W. W. A new error analysis of characteristics-mixed FEMs for miscible displacement in porous media. SIAM Journal on Numerical Analysis, 52, 3000-3020(2014)
[26] Ingram, R. A new linearly extrapolated Crank-Nicolson time-stepping scheme for the NavierStokes equations. Mathematics of Computation, 82, 1953-1973(2013) |