A Parallel Finite Element Algorithm for the Unsteady Oseen Equations

[1]  Rolf Rannacher,et al.  Finite element approximation of the nonstationary Navier-Stokes problem, part III. Smoothing property and higher order error estimates for spatial discretization , 1988 .

[2]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[3]  Yinnian He,et al.  The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data , 2008, Math. Comput..

[4]  Yueqiang Shang.  A parallel two-level finite element variational multiscale method for the Navier–Stokes equations ☆ , 2013 .

[5]  Yueqiang Shang,et al.  Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations , 2010, Numerical Algorithms.

[6]  Jinchao Xu,et al.  Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems , 2001, Adv. Comput. Math..

[7]  Guangzhi Du,et al.  Local and parallel finite element post-processing scheme for the Stokes problem , 2017, Comput. Math. Appl..

[8]  R. Rannacher,et al.  Finite element approximation of the nonstationary Navier-Stokes problem. I : Regularity of solutions and second-order error estimates for spatial discretization , 1982 .

[9]  Yueqiang Shang,et al.  A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations , 2021 .

[10]  Feng Shi,et al.  Local and Parallel Finite Element Algorithms Based on the Partition of Unity for the Stokes Problem , 2014, SIAM J. Sci. Comput..

[11]  Frédéric Hecht,et al.  New development in freefem++ , 2012, J. Num. Math..

[12]  Guangzhi Du,et al.  A parallel partition of unity method for the nonstationary Navier-Stokes equations , 2017 .

[13]  Guangzhi Du,et al.  Local and parallel finite element methods for the coupled Stokes/Darcy model , 2020, Numerical Algorithms.

[14]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[15]  Yueqiang Shang,et al.  Parallel finite element variational multiscale algorithms for incompressible flow at high Reynolds numbers , 2017 .

[16]  Yanren Hou,et al.  A parallel partition of unity method for the unsteady Stokes equations , 2017 .

[17]  Jinchao Xu,et al.  Local and parallel finite element algorithms based on two-grid discretizations , 2000, Math. Comput..

[18]  Jinchao Xu,et al.  Local and Parallel Finite Element Algorithms for Eigenvalue Problems , 2002 .

[19]  Yueqiang Shang,et al.  Local and Parallel Finite Element Algorithms for the Stokes Equations with Nonlinear Slip Boundary Conditions , 2019, International Journal of Computational Methods.

[20]  L. Wahlbin.  Superconvergence in Galerkin Finite Element Methods , 1995 .

[21]  Endre Süli,et al.  Approximation of the global attractor for the incompressible Navier–Stokes equations , 2000 .

[22]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .

[23]  Hai Bi,et al.  Local and Parallel Finite Element Algorithms for the Transmission Eigenvalue Problem , 2018, Journal of Scientific Computing.

[24]  Jinchao Xu,et al.  Local and parallel finite element algorithms for the stokes problem , 2008, Numerische Mathematik.