The Semi-Discrete Finite Element Method for the Cauchy Equation

Lei Hou; Xian Yan Sun; Lin Qiu

doi:10.4028/www.scientific.net/AMM.668-669.1130

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 668-669The Semi-Discrete Finite Element Method for the...

The Semi-Discrete Finite Element Method for the Cauchy Equation

Abstract:

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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Periodical:

Applied Mechanics and Materials (Volumes 668-669)

Pages:

1130-1133

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.668-669.1130

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Online since:

October 2014

Authors:

Lei Hou*, Xian Yan Sun, Lin Qiu

Keywords:

Cauchy Equation, Convergence, Crank-Nicolson Scheme, Lagrange Interpolation Function, Semi-Discrete Finite Element

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References

[1] Hou L, R. Harwood, Nonlinear properties in the Newtonian and Non-Newtonian Equations. Nonlinear analysis, 30(4): 497-2505(1997).

DOI: 10.1016/s0362-546x(96)00226-x

Google Scholar

[2] Hou L, Cai L. Nonlinear Property of the visco-elastic-plastic material in the impact problem[J]. Journal of Shanghai University(English Edition), 01: 23-28(2009).

DOI: 10.1007/s11741-009-0106-3

Google Scholar

[3] Hou L, Zhao J, Li H. Finite element convergence analysis of two-scale non-Newtonian flow problems. Proceedings of Advances Materials Research. Xiamen, China, 1723-1728(2013).

DOI: 10.4028/www.scientific.net/amr.718-720.1723

Google Scholar

[4] Bai D, Zhang L. The finite element method for the coupled Schrodinger-KdV equations. Physics Letters A2237-2244 (2009).

Google Scholar

[5] IOHNSON C. Numerical solution of partial differential equations by the finite element method[M]. [S.I. ]: courier Dover publications(2012).

Google Scholar

[6] CHORIN A J. Numerical solution of the Naiver-Stokes equations[J]. Mathematics of computation, 22(104): 745-762(1968).

DOI: 10.1090/s0025-5718-1968-0242392-2

Google Scholar

[7] BRENNER S C, SCOTT R. The mathematical theory of finite element methods[M]. Vol. 15. [S.I. ]: Springer(2008).

Google Scholar

[8] NICHOLS B, HIRT C, HOTCHKISS R. SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries[J]. NASA STI/Recon Technical Report N, 81: 14281(1980).

DOI: 10.2172/5122053

Google Scholar