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 - <p style="text-align: justify;">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.</p>