A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations
Year: 2023
Author: Shaohong Du, Qianqian Hou, Xiaoping Xie
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0018
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 323–351
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Convection-diffusion-reaction equation dynamical diffusion method residual-type a posteriori error estimator adaptive algorithm.