A Posteriori Error Estimation and Adaptive Algorithm for Singularly Perturbed Reaction-Diffusion Equations

BAO Xiaobing; LIU Libin; MAO Zhi

doi:10.21656/1000-0887.410103

Volume 42 Issue 3

Mar. 2021

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BAO Xiaobing, LIU Libin, MAO Zhi. A Posteriori Error Estimation and Adaptive Algorithm for Singularly Perturbed Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(3): 323-330. doi: 10.21656/1000-0887.410103

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A Posteriori Error Estimation and Adaptive Algorithm for Singularly Perturbed Reaction-Diffusion Equations

doi: 10.21656/1000-0887.410103

¹School of Big Data and Artificial Intelligence, Chizhou University, Chizhou, Anhui 247000, P.R.China
²School of Mathematics and Statistics, Nanning Normal University, Nanning 530100, P.R.China
³School of Data Science, Tongren University, Tongren, Guizhou 554300, P.R.China

Funds: The National Natural Science Foundation of China（11761015）

Received Date: 2020-04-09
Rev Recd Date: 2020-12-29
Publish Date: 2021-03-01

Abstract

Abstract

An adaptive grid method for singularly perturbed semilinear reactiondiffusion equations was studied. The equation was discretized by means of the upwind finite difference scheme on an arbitrary nonuniform mesh. A posteriori error estimation of the presented numerical scheme was built. In turn, the posteriori error bound was derived, and the adaptive grid generation algorithm was designed. Numerical experiments prove the effectiveness of the proposed adaptive grid method.
- singular perturbation,
- posteriori error,
- adaptive moving grid,
- reaction-diffusion equation

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References(18)

References

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