For convection-diffusion-reaction equations, we are interested in the dynamic diffusion (DD) method, which is free of stabilization parameters and capable of precluding numerical oscillations, and prove the existence and uniqueness of the approximation solution for the DD method by applying the contraction mapping principle. In the energy norm, we propose a residual-type a posteriori error estimator, which is proven to be reliable and efficient, and which is robust when the local Péclet number is not large. Based on the a posteriori estimator, we develop a linearized adaptive DD (LADD) algorithm, and carry out numerical experiments to validate the effectiveness and reliability of the LADD algorithm.
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Funding
The Scientific and Technological Research Program of Chongqing Municipal Education(KJZD-M202300705)
The Natural Science Foundation of Chongqing(CSTB2025NSCQ-GPX0873)
RIGHTS & PERMISSIONS
Shanghai University
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