In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding 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.

翻译：本文针对对流-扩散-反应方程，提出了一种修正的非线性动态扩散有限元方法。该方法无需稳定化参数，且能够有效抑制数值振荡。我们证明了离散解的存在性，并在网格尺寸足够小的假设下证明了其唯一性，同时推导了能量范数与耗散项之和的近似误差的最优一阶收敛速度。数值算例验证了理论分析结果。