Finite element method for solving nonlinear inverse diffusion problem

Zeidabadi, Hamed; pourgholi, Reza; Tabasi, S. Hashem

doi:10.52547/mmr.7.2.291

Volume 7, Issue 2 (Vol.7, No. 2, 2021) mmr 2021, 7(2): 291-310 | Back to browse issues page

‎ 10.52547/mmr.7.2.291

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Zeidabadi H, pourgholi R, Tabasi S H. Finite element method for solving nonlinear inverse diffusion problem. mmr 2021; 7 (2) :291-310
URL: http://mmr.khu.ac.ir/article-1-2654-en.html

Finite element method for solving nonlinear inverse diffusion problem

Hamed Zeidabadi¹

, Reza Pourgholi

², S. Hashem Tabasi³

1- Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran
2- School of Mathematics and Computer Science, Damghan University, Damghan, Iran , pourgholi@du.ac.ir
3- School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract: (1264 Views)

In this paper, a numerical method based on the finite element method and the least square scheme with the Tikhonov regularization method for nonlinear inverse diffusion problem is presented. For this propose, first finite element method and basis functions will be used to discretize the variational form of the problem; then the least square scheme and Tikhonov regularization method are proposed to correct diffusion. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, and so, it is classified as the function estimation in inverse calculation. Numerical result shows that a good estimation on the unknown functions of the inverse problem can be obtained../files/site1/files/72/9Abstract.pdf

Keywords: Nonlinear inverse diffusion problem, Finite element method, Least square method, Tikhonov regularization method, Error estimation.

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