1 |
R. H. Nochetto and J.-H. Pyo, The gauge-Uzawa finite element method. I. The Navier-Stokes equations, SIAM J. Numer. Anal. 43 (2005), no. 3, 1043–1068
DOI
ScienceOn
|
2 |
J.-H. Pyo and J. Shen, Gauge-Uzawa methods for incompressible flows with variable density, J. Comput. Phys. 221 (2007), no. 1, 181–197
DOI
ScienceOn
|
3 |
R. B. Kellogg and J. E. Osborn, A regularity result for the Stokes problem in a convex polygon, J. Functional Analysis 21 (1976), no. 4, 397–431
DOI
|
4 |
R. H. Nochetto and J.-H. Pyo, Optimal relaxation parameter for the Uzawa method, Numer. Math. 98 (2004), no. 4, 695–702
DOI
|
5 |
Weinan E. and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci. 1 (2003), 317–332
|
6 |
V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, 5. Springer-Verlag, Berlin, 1986
|
7 |
J. G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization, SIAM J. Numer. Anal. 19 (1982), no. 2, 275–311
|
8 |
P. Constantin and C. Foias, Navier-Stokes Equations, The University of Chicago Press, 1988
|
9 |
R. H. Nochetto and J.-H. Pyo, Error estimates for semi-discrete gauge methods for the Navier-Stokes equations, Math. Comp. 74 (2005), no. 250, 521–542
DOI
ScienceOn
|
10 |
A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp. 22(1968), 745–762
|
11 |
M. Dauge, Stationary Stokes and Navier-Stokes systems on two- or three-dimensional domains with corners. I. Linearized equations, SIAM J. Math. Anal. 20 (1989), no.1, 74–97
DOI
|
12 |
J.-H. Pyo and J. Shen, Normal mode analysis of second-order projection methods for incompressible flows, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), no. 3, 817–840
|
13 |
R. H. Nochetto and J.-H. Pyo, The gauge-Uzawa finite element method. II. The Boussinesq equations, Math. Models Methods Appl. Sci. 16 (2006), no. 10, 1599–1626
|
14 |
A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations, Advances in Numerical Mathematics. B. G. Teubner, Stuttgart, 1997
|
15 |
J.-H. Pyo, The gauge-Uzawa and related projection finite element methods for the evolution Navier-Stokes equations, Ph.D. dissertation, University of Maryland, 2002
|
16 |
R. T´emam, Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires. II, Arch. Rational Mech. Anal. 33 (1969), 377–385
|
17 |
C. Wang and J.-G. Liu, Convergence of gauge method for incompressible flow, Math. Comp. 69 (2000), no. 232, 1385–1407
DOI
ScienceOn
|
18 |
D. L. Brown, R. Cortez, and M. L. Minion, Accurate projection methods for the incompressible Navier-Stokes equations, J. Comput. Phys. 168 (2001), no. 2, 464–499
DOI
ScienceOn
|