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An H1-Galerkin Mixed Method for the Coupled Burgers Equation
In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.
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[1] R C Mittal, G Arora. Numerical solution of the coupled viscous Burgers- equation, Communications in Nonlinear Science and Numerical Simulation, 2010, 16(3): 1304-1313.
[2] A K Pani. An H1-Galerkin mixed finite element methods for parabolic partial differential equations, SIAM J. Numer. Anal., 1998, 35: 712-727.
[3] A K Pani, G Fairweather. H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations, IMA Journal of Numerical Analysis., 2002,22: 231-252.
[4] D Y Shi, H H Wang. An H1-Galerkin nonconforming mixed finite element method for integro-differential equation of parabolic type, Journal of Mathematical Research & Exposition, 2009, 29(5): 871-881.
[5] R W Wang. Error estimates for H1-Galerkin mixed finite element methods hyperbolic type integro- differential equation, Math. Numer. Sin., 2006, 28(1): 20-30. (in Chinese)
[6] Y Liu, H Li, S He. Error estimates of H1-Galerkin mixed finite element methods for pseudo-hyperbolic partial integro-differential equation, Numerical Mathematics A Journal of Chinese Universities, 2010, 32(1): 1-20.(in Chinese)
[7] L Guo, H Z Chen. H1-Galerkin mixed finite element methods for the Sobolev equation, Journal of Systems Science and Mathematical Sciences, 2006, 26(3): 301-314.(in Chinese)
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[12] J F Wang, Y Liu, H Li, X Y Li. H1-Galerkin mixed element method for the coupling nonlinear parabolic partial equations, Pure Mathematics, 2011, 1(2): 73-79.(in Chinese)
[13] Y Liu, H Li, J F Wang. Error estimates of H1-Galerkin mixed finite element method for Schr¨odinger equation. Appl. Math. J. Chinese Univ. 2009, 24(1): 83-89.
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[15] Y. Liu. Analysis and numerical simulation of nonstandard mixed element methods, PhD thesis, Inner Mongolia University, Hohhot, China, 2011.
[16] A K Pani, R K Sinha, A K Otta. An H1-Galerkin mixed method for second order hyperbolic equations, Inter Journal of Numerical Anal and Modeling., 2004,1(2): 111-129.
[17] H Z Chen, H Wang. An optimal-order error estimate on an H1-Galerkin mixed method for a nonlinear parabolic equation in porous medium flow, Numer. Methods Partial Differential Equations, 2010, 26: 188-205.
[18] H T Che, Y J Wang, Z J Zhou. An optimal error estimates of H1-Galerkin expanded mixed finite element methods for nonlinear viscoelasticity-type equation, Mathematical Problems in Engineering, Volume 2011, Article ID 570980, 18 pages. doi:10.1155/2011/570980.
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