The Super-Convergence in Rheological Flow

L. HOU, S. L. ZHOU, X. Y. SUN, J. J. ZHAO, L. QIU, H. L. LI


To estimate the solution of the coupled first-order hyperbolic partial differential equations, we use both the boundary-layer method and numeric analysis to study the Cauchy fluid equations and P-T/T stress equation.  On the macroscopic scale the free surface elements generate flow singularity and stress uncertainty by excessive tensile stretch. A numerical super-convergence semi-discrete finite element scheme is used to solve the time dependent equations. The coupled nonlinear solutions are estimated by boundary-layer approximation. Its numerical super convergence is proposed with the a priori and a posteriori error estimates.


Non-Newtonian fluid; Semi-discrete finite element method; Super convergence; Boundary-layer solution

Full Text:



[1] Hou, L., & Vahid, N. (2001). Evaluation of stress affects flow in rubber mixing. Nonlinear analysis, Elsevier Sciences, 47(3), 1809-1820.

[2] Hou, L., Li, H., Zhang, J. J., Lin, D. Z., & Qiu, L. (2010). Boundary-layer eigen solutions for multi-field coupled equations in the contact interface. Applied Mathematics Appl. Math. Mech. (English Ed). 31(6), 719–732.

[3] Hou, L., & Qiu, L. (2009). Computation and asymptotic analysis in the impact problem. Acta Mathematic Applica Sinica, English Series, 25(1), 117–126. doi: 10.1007/s10255-007-7158-7

[4] Hou, L., Zhao, J., & Li, H. L. (2013). Finite element convergence analysis of two-scale non-newtonian flow problems. Advanced Materials Research, 718-720, 1723-1728.

[5] Lin, Q., & Yan, N. N. (1996). Superconvergence of mixed finite element methods for Maxwell’s equations. Engineering Mathematics, 13(12), 1-10.

[6] Hou, L., & Nassehi, V. (2001). Evaluation of stress-effective flow in rubber mixing. Nonlinear Analysis, 47(3), 1809-1820.

[7] Hou, L., Lin, D. Z., & Li, H. L. (2011). Computational modeling on the complex boundary conditions in the impact problem. International Conference on Computer and Network Technology, 4, 231-235.

[8] Zhu, C. D., & Lin, Q. (1989). Finite element super-convergence theory. Hunan Science and Technology Press.




  • There are currently no refbacks.

Copyright (c)

Share us to:   


If you have already registered in Journal A and plan to submit article(s) to Journal B, please click the "CATEGORIES", or "JOURNALS A-Z" on the right side of the "HOME".

We only use the follwoing mailboxes to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:

 Articles published in Progress in Applied Mathematics are licensed under Creative Commons Attribution 4.0 (CC-BY).


Address: 1020 Bouvier Street, Suite 400, Quebec City, Quebec, G2K 0K9, Canada.

Telephone: 1-514-558 6138

Copyright © 2010 Canadian Research & Development Center of Sciences and Cultures