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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} }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.