HOU Lei, SUN Xian-yan, ZHAO Jun-jie, LI Han-ling. Convergence of Finite Element Method in Rheology[J]. Applied Mathematics and Mechanics, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007
Citation: HOU Lei, SUN Xian-yan, ZHAO Jun-jie, LI Han-ling. Convergence of Finite Element Method in Rheology[J]. Applied Mathematics and Mechanics, 2014, 35(4): 412-422. doi: 10.3879/j.issn.1000-0887.2014.04.007

Convergence of Finite Element Method in Rheology

doi: 10.3879/j.issn.1000-0887.2014.04.007
Funds:  The National Natural Science Foundation of China(11271247)
  • Received Date: 2013-10-18
  • Rev Recd Date: 2014-03-13
  • Publish Date: 2014-04-15
  • Convergence of the first-order mixed-type hyperbolic parabola partial differential equations in non-Newtonian fluid problems was studied. The coupling partial differential equations (Cauchy fluid equation, P-T/T stress equation) were used to simulate the flow zone generated by the free surface elements or excessively tensile elements. The semi-discrete finite element method was applied to solve these equations coupling with time. The finite element method was used in space. The trilinear functional was employed to solve the nonlinear problems of partial differential equations. In the time domain the Euler scheme was adopted. The convergence order of the equation set reached O(h2+Δt). Numerical results of the equations were obtained through priori and posteriori error estimation of high performance computation. And the deformed sizes of the grids were presented.
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