This article focuses on discretizing the convection–diffusion–reaction equation (concentration or heat), which is time-dependent and coupled with the Darcy equation. The Darcy system is discretized using the Raviart–Thomas finite element, while the concentration equation is discretized using the Lagrange finite element of order one in space and the Euler method in time. We present optimal a posteriori error estimates utilizing two computable error indicators: linearization and discretization indicators. Ultimately, numerical experiments demonstrate and confirm the efficacy of the proposed method, and show comparisons with previous works.

中文翻译：

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与 Raviart-Thomas 有限元离散的达西系统耦合的非平稳浓度方程的后验误差估计

本文重点关注对流-扩散-反应方程（浓度或热量）的离散化，该方程与时间相关并与达西方程耦合。达西系统采用 Raviart–Thomas 有限元进行离散，而浓度方程在空间上采用一阶拉格朗日有限元，在时间上采用欧拉法进行离散。我们利用两个可计算的误差指标提出最佳后验误差估计：线性化和离散化指标。最终，数值实验证明并证实了所提出方法的有效性，并与之前的工作进行了比较。