Volume 39, Issue 3
A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations

Shaohong Du, Qianqian Hou & Xiaoping Xie

Ann. Appl. Math., 39 (2023), pp. 323-351.

Published online: 2023-09

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  • Abstract

In this paper, we consider a modified nonlinear dynamic diffusion (DD) method for convection-diffusion-reaction equations. This method is free of stabilization parameters and capable of precluding spurious oscillations. We develop a reliable and efficient residual-type a posteriori error estimator, which is robust with respect to the diffusivity parameter. Furthermore, we propose a linearized adaptive DD algorithm based on the a posteriori estimator. Finally, we perform numerical experiments to verify the theoretical analysis and the performance of the adaptive algorithm.

  • AMS Subject Headings

65K10, 65N30, 65N21, 49M25, 49K20

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COPYRIGHT: © Global Science Press

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@Article{AAM-39-323, author = {Du , ShaohongHou , Qianqian and Xie , Xiaoping}, title = {A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations}, journal = {Annals of Applied Mathematics}, year = {2023}, volume = {39}, number = {3}, pages = {323--351}, abstract = {

In this paper, we consider a modified nonlinear dynamic diffusion (DD) method for convection-diffusion-reaction equations. This method is free of stabilization parameters and capable of precluding spurious oscillations. We develop a reliable and efficient residual-type a posteriori error estimator, which is robust with respect to the diffusivity parameter. Furthermore, we propose a linearized adaptive DD algorithm based on the a posteriori estimator. Finally, we perform numerical experiments to verify the theoretical analysis and the performance of the adaptive algorithm.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0018}, url = {http://global-sci.org/intro/article_detail/aam/21996.html} }
TY - JOUR T1 - A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations AU - Du , Shaohong AU - Hou , Qianqian AU - Xie , Xiaoping JO - Annals of Applied Mathematics VL - 3 SP - 323 EP - 351 PY - 2023 DA - 2023/09 SN - 39 DO - http://doi.org/10.4208/aam.OA-2023-0018 UR - https://global-sci.org/intro/article_detail/aam/21996.html KW - Convection-diffusion-reaction equation, dynamical diffusion method, residual-type a posteriori error estimator, adaptive algorithm. AB -

In this paper, we consider a modified nonlinear dynamic diffusion (DD) method for convection-diffusion-reaction equations. This method is free of stabilization parameters and capable of precluding spurious oscillations. We develop a reliable and efficient residual-type a posteriori error estimator, which is robust with respect to the diffusivity parameter. Furthermore, we propose a linearized adaptive DD algorithm based on the a posteriori estimator. Finally, we perform numerical experiments to verify the theoretical analysis and the performance of the adaptive algorithm.

Du , ShaohongHou , Qianqian and Xie , Xiaoping. (2023). A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations. Annals of Applied Mathematics. 39 (3). 323-351. doi:10.4208/aam.OA-2023-0018
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