[1] Adams R A. Sobolev Spaces. New York:Academic Press, 1975
[2] Alekseev A K, Navon I M, Steward J L. Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems. Optimization Methods & Software, 2009, 24(1):63-87
[3] An J, Sun P, Luo Z D, Huang X M. A stabilized fully discrete finite volume element formulation for non-stationary Stokes equations. Math Numer Sin, 2011, 33(2):213-224
[4] Bourgault Y, Caussignac P, Renggli L. Finite element methods for parabolized Navier-Stokes equations. Comput Methods Appl Mech Eng, 1994, 111(3/4):265-282
[5] Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods. New York:Springer-Verlag, 1991
[6] Ciarlet P G. The Finite Element Method for Elliptic Problems. Amsterdam:North-Holland, 1978
[7] D'Ambrosio D, Marsilio R. A numerical method for solving the three-dimensional parabolized Navier-Stokes equations. Computers & Fluids, 1997, 26(6):587-611
[8] Gao Z. Significance and use of basic equation system governing high Reynolds number flows and diffusion-parabolized Navier-Stokes equations. Adv Mech, 2005, 35(3):427-438
[9] Girault V, Raviart P A. Finite Element Methods for Navier-Stokes Equations:Theory and Algorithms. Berlin Heidelberg:Springer-Verlag, 1986
[10] He G L, He Y N, Feng X L. Finite volume method based on stabilized finite elements for the non-stationary Navier-Stokes problem. Numerical Methods for Partial Differential Equations, 2007, 23(5):1167-1191
[11] He Y, Lin Y, Sun W. Stabilized finite element method for the non-stationary Navier-Stokes problem. Disc Cont Dyn Syst B, 2006, 6(1):41-68
[12] Heywood J G, Rannacher R. Finite element approximation of the non-stationary Navier-Stokes problem, I. Regularity of solutions and second order estimates for spatial discretization. SIAM J Num Anal, 1982, 19(2):275-311
[13] Heywood J G, Rannacher R. Finite element approximation of the non-stationary Navier-Stokes problem part IV:error analysis for second-order time discretization. SIAM J Num Anal, 1990, 27(2):353-384
[14] Jones W P, Menziest K R. Analysis of the cell-centred finite volume method for the diffusion equation. J Comput Phys, 2000, 165(1):45-68
[15] Li R H, Chen Z Y, Wu W. Generalized Difference Methods for Differential Equations-Numerical Analysis of Finite Volume Methods. Monographs and Textbooks in Pure and Applied Mathematics 226. New York:Marcel Dekker Inc, 2000
[16] Li J, Chen Z X. A new stabilized finite volume method for the stationary Stokes equations. Adv Comput Math, 2009, 30:141-152
[17] Li H R, Luo Z D, Li Q. Generalized difference methods for two-dimensional viscoelastic problems. Chinese J Numer Math Appl, 2007, 29(3):251-262
[18] Luo Z D. The Foundations and Applications of Mixed Finite Element Methods. Beijing:Science Press, 2006(in Chinese)
[19] Luo Z D. A stabilized Crank-Nicolson mixed finite element method for the non-stationary parabolized Navier-Stokes equations. Acta Mathematica Applicatae Sinica, in press (Accepted for publication)
[20] Pratap V S, Spalding D B. Fluid flow and heat transfer in three-dimensional duct flows. Int J Heat Mass Transfer, 1976, 19:1183-1188
[21] Shen L H, Li J, Chen Z X. Analysis of a stabilized finite volume method for the transient stationary Stokes equations. Int J Numer Anal Model, 2009, 6:505-519
[22] Temam R. Navier-Stokes Equations. 3rd ed. New York:North-Holland, Amsterdam, 1984
[23] Wang R, Shen Y. Numerical solutions of the diffusion parabolized Navier-Stokes Equations. Adv Mech, 2005, 35(4):481-497
[24] Zhang H, Guo C, Zong W. Problems about gird and high order schemes. Chinese J Theoretical Appl Mech, 1999, 31(4):398-405
[25] Zhang H, Yu Z, Lu L, Ma Z. Numerical solutions of supersonic and hypersonic laminar separated flow. Chinese J Theoretical Appl Mech, 1981, 13(4):333-345 |