Global existence, uniqueness and optimal solvers of discretized viscoelastic flow models

作者: YOUNG-JU LEE , JINCHAO XU , CHEN-SONG ZHANG

DOI: 10.1142/S0218202511005544

关键词:

摘要: This paper is devoted to studying the well-posedness and optimal solution techniques for a full discretization scheme, proposed by Lee Xu (2006), large class of viscoelastic flow models. By using some special properties scheme such that it stable in energy norm preserves positivity conformation tensor, global existence uniqueness discrete established. Furthermore, shown at each time step can be obtained an iterative procedure only requires operations (with N being number nodes underlying finite element grid).

参考文章(33)
L. R. Scott, M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials Mathematical Modelling and Numerical Analysis. ,vol. 19, pp. 111- 143 ,(1985) , 10.1051/M2AN/1985190101111
Min-Jung Ahn, Hyun-Young Lee, AN EXISTENCE OF THE FULLY DISCRETE SOLUTION FOR THE NAVIER STOKES EQUATION Communications of The Korean Mathematical Society. ,vol. 14, pp. 833- 842 ,(1999)
Feng Kang, Shang Zai-jiu, Volume-preserving algorithms for source-free dynamical systems Numerische Mathematik. ,vol. 71, pp. 451- 463 ,(1995) , 10.1007/S002110050153
G. Lielens, P. Halin, I. Jaumain, R. Keunings, V. Legat, New closure approximations for the kinetic theory of finitely extensible dumbbells Journal of Non-newtonian Fluid Mechanics. ,vol. 76, pp. 249- 279 ,(1998) , 10.1016/S0377-0257(97)00121-3
F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique. ,vol. 8, pp. 129- 151 ,(1974) , 10.1051/M2AN/197408R201291
Jean Roberts, Jean-Marie Thomas, Mixed and hybrid finite element methods Springer-Verlag. ,(1991) , 10.1007/978-1-4612-3172-1
Young-Ju Lee, Jinchao Xu, New formulations, positivity preserving discretizations and stability analysis for non-newtonian flow models Computer Methods in Applied Mechanics and Engineering. ,vol. 195, pp. 1180- 1206 ,(2006) , 10.1016/J.CMA.2005.04.008
Andrew J. Szeri, A deformation tensor model for nonlinear rheology of FENE polymer solutions Journal of Non-Newtonian Fluid Mechanics. ,vol. 92, pp. 1- 25 ,(2000) , 10.1016/S0377-0257(00)00090-2
M. Grmela, P.J. Carreau, Conformation tensor rheological models Journal of Non-newtonian Fluid Mechanics. ,vol. 23, pp. 271- 294 ,(1987) , 10.1016/0377-0257(87)80022-8
Torgeir Rusten, Ragnar Winther, A preconditioned iterative method for saddlepoint problems SIAM Journal on Matrix Analysis and Applications. ,vol. 13, pp. 887- 904 ,(1992) , 10.1137/0613054