An H1-Galerkin Mixed Method for the Coupled Burgers Equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32805
An H1-Galerkin Mixed Method for the Coupled Burgers Equation

Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

Abstract:

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.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1056805

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1511

References:


[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)
[8] D Y Shi, H H Wang, Nonconforming H1-Galerkin mixed FEM for Sobolev equations on anisotropic Meshes, Acta Mathematicae Applicatae Sinica (English Series), 2009, 25(2): 335-344.
[9] Y Liu, H Li. H1-Galerkin mixed finite element methods for pseudohyperbolic equations, Appl. Math. Comput., 2009, 212: 446-457.
[10] Y Liu, J F Wang, H Li, W Gao, S He. A new splitting H1-Galerkin mixed method for pseudo-hyperbolic equations, International Journal of Engineering and Natural Sciences, 2011, 5(2): 58-63.
[11] Z J Zhou. An H1-Galerkin mixed finite element method for a class of heat transport equations, Applied Mathematical Modelling, 2010, 34(9): 2414-2425.
[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.
[14] Y Liu, H Li. A new mixed finite element method for pseudo-hyperbolic equation, Mathematica Applicata, 2010, 23(1): 150-157.
[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.
[19] M F Wheeler. A priori L2-error estimates for Galerkin approximations to parabolic differential equation, SIAM J. Numer. Anal.,1973, 10: 723- 749.