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Nonconforming Mixed Finite Element Method for Nonlinear Hyperbolic Equations

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DOI: 10.4236/am.2012.33037    5,365 Downloads   8,077 Views  

ABSTRACT

A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

H. Wang and C. Guo, "Nonconforming Mixed Finite Element Method for Nonlinear Hyperbolic Equations," Applied Mathematics, Vol. 3 No. 3, 2012, pp. 231-234. doi: 10.4236/am.2012.33037.

References

[1] T. Dupont, “L2-Estimates for Galerkin Methods for Second Order Hyperbolic Equations,” SIAM Journal on Numerical Analysis, Vol. 10, No. 1, 1973, pp. 880-889. doi:10.1137/0710073
[2] T. Oden and J. Reddy, “An Introduction to the Mathematical Theory of Finite Elements,” Wiley Interscience, New York, 1976.
[3] G. A. Baker, “Error Estimates for Finite Element Methods for Second Hyperbolic Equations,” SIAM Journal on Numerical Analysis, Vol. 13, No. 1, 1976, pp. 564-576. doi:10.1137/0713048
[4] J. J. Douglas, “Superconvergence in the Pressure in the Simulation of Miscible Displacement,” SIAM Journal on Numerical Analysis, Vol. 22, No. 1, 1985, pp. 962-969. doi:10.1137/0722058
[5] L. C. Cowsar, T. F. Dupont and M. T. Wheeler, “A Priori Estimates for Mixed Finite Element Approximations of second-order Hyperbolic Equations with Absorbing Boundary Conditions,” Computer Methods in Applied Mechanic and Engineering, Vol. 33, No. 1, 1996, pp. 492-504.
[6] Y. P. Chen and Y. Q. Huang, “Mixed Finite Element Method for Nonlinear Hyperbolic Equations,” Numerical Mathematics A Journal of Chinese University, Vol. 1, 2000, pp. 63-69.
[7] S. Martin and T. Lutz, “The Streamline-Diffusion Method for Nonconforming Qrot Elements on Rectangular Tensor-Product,” IMA Journal Numerical Analysis, Vol. 21, No. 1, 2001, pp: 123-142. doi:10.1093/imanum/21.1.123
[8] J. K. Hale, “Ordinary Differential Equations,” WilleyInterscience, New York, 1969.
[9] D. Y. Shi and H. H. Wang, “Nonconforming H1-Galerkin Mixed FEM for Sobolev Equations on Anisotropic Meshes,” Acta Mathematicae Applicatae Sininica, Vol. 25, No. 2B, 2009, pp. 335-344. doi:10.1007/s10255-007-7065-y
[10] P. G. Ciarlet, “The Finite Element Method for Elliptic Problem,” North-Holland, Amsterdam, 1978.

  
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