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Meshfree method for the non-stationary incompressible Navier-Stokes equations
Stabilized finite element method for the non-stationary Navier-Stokes problem
1. | Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China |
2. | Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1 |
3. | Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China |
[1] |
Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222 |
[2] |
Eid Wassim, Yueqiang Shang. Local and parallel finite element algorithms for the incompressible Navier-Stokes equations with damping. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022022 |
[3] |
Konstantinos Chrysafinos. Error estimates for time-discretizations for the velocity tracking problem for Navier-Stokes flows by penalty methods. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1077-1096. doi: 10.3934/dcdsb.2006.6.1077 |
[4] |
Xiaoxiao He, Fei Song, Weibing Deng. A stabilized nonconforming Nitsche's extended finite element method for Stokes interface problems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2849-2871. doi: 10.3934/dcdsb.2021163 |
[5] |
Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1277-1289. doi: 10.3934/dcdss.2013.6.1277 |
[6] |
Grzegorz Karch, Maria E. Schonbek, Tomas P. Schonbek. Singularities of certain finite energy solutions to the Navier-Stokes system. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 189-206. doi: 10.3934/dcds.2020008 |
[7] |
Gianmarco Manzini, Annamaria Mazzia. A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem. Journal of Computational Dynamics, 2022, 9 (2) : 207-238. doi: 10.3934/jcd.2021020 |
[8] |
Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609 |
[9] |
Hantaek Bae. Solvability of the free boundary value problem of the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 769-801. doi: 10.3934/dcds.2011.29.769 |
[10] |
Yinnian He, Kaitai Li. Nonlinear Galerkin approximation of the two dimensional exterior Navier-Stokes problem. Discrete and Continuous Dynamical Systems, 1996, 2 (4) : 467-482. doi: 10.3934/dcds.1996.2.467 |
[11] |
Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602 |
[12] |
Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149 |
[13] |
Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control and Related Fields, 2021, 11 (3) : 601-624. doi: 10.3934/mcrf.2021014 |
[14] |
Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations and Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1 |
[15] |
Jean-Pierre Raymond, Laetitia Thevenet. Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1159-1187. doi: 10.3934/dcds.2010.27.1159 |
[16] |
Xufeng Xiao, Xinlong Feng, Jinyun Yuan. The stabilized semi-implicit finite element method for the surface Allen-Cahn equation. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2857-2877. doi: 10.3934/dcdsb.2017154 |
[17] |
Juan Wen, Yaling He, Yinnian He, Kun Wang. Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations. Communications on Pure and Applied Analysis, 2022, 21 (6) : 1873-1894. doi: 10.3934/cpaa.2021074 |
[18] |
Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1641-1670. doi: 10.3934/dcdsb.2010.14.1641 |
[19] |
Jie Shen, Xiaofeng Yang. Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 663-676. doi: 10.3934/dcdsb.2007.8.663 |
[20] |
Francesca Crispo, Paolo Maremonti. A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1283-1294. doi: 10.3934/dcds.2017053 |
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