A Linearized Adaptive Dynamic Diffusion Finite Element Method for Convection-Diffusion-Reaction Equations

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.