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This development reports optimal convergence rates in convection-diffusion-reaction equations, suggesting advancements in computational methods.
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method (FEM) for convection‐diffusion‐reaction equations. This method is free of stabilization parameters and is capable of suppressing spurious oscillations. We prove existence and, under an assumption of small mesh size, uniqueness of the discrete solution, and derive the optimal first‐order convergence rate of the approximation error in the energy norm plus a dissipation term. Numerical examples are provided to verify the theoretical analysis.
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Du et al. (2026) studied this question.
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