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<p>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.</p>

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Residual-Based a Posteriori Error Estimator for Dynamic Diffusion Method for Convection-Diffusion-Reaction Equations

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Shaohong Du,
  • Guilin Pan,
  • Sheng Wang,
  • Qian Hou

摘要

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.