Abstract
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.
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References
Todenes O. On the Numerical Solution of the Diffusion Equation.Math Comput, 1970,24(111):621–635.
Oden J T, Redby J N.An Introduction to the Mathematical Theory of Finite Elements. New York: Wiley, 1976.
Onah E S. Asymptotic Behaviour of the Galerkin and the Finite Element Collocation Methods for a Parabolic Equation.J App Math Comput, 2002,127: 207–213.
Fried I.Numerical Solution of Differential Equations. New York: Academic Press, 1979.
Wiley J.Numerical Solution of Differential Equations. New York: Halsted Press, 1984.
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Foundation item: Supported by the National Natural Science Foundation of China (10101018)
Biography: Liu Yang (1978-), male, Master, research direction: numerical solution of partial differential equations.
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Yang, L., Hui, F. Asymptotic behavior of the finite difference and the finite element methods for parabolic equations. Wuhan Univ. J. Nat. Sci. 10, 953–956 (2005). https://doi.org/10.1007/BF02832446
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DOI: https://doi.org/10.1007/BF02832446