In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general choice of the limiter, which defines the nonlinear stabilization term. In the diffusion-dominated regime, the estimator has the same convergence properties as the true error. A second approach is discussed, where the upper bound is derived in a posteriori way using the Streamline Upwind Petrov Galerkin (SUPG) estimator proposed in [20]. Numerical examples study the effectivity index and the adaptive grid refinement for two limiters in two dimensions.

在这项工作中，我们为平稳对流扩散方程的代数通量校正 (AFC) 方案提出了一种基于残差的后验误差估计器。为限制器的一般选择的能量范数中的误差导出全局上限，该限制器定义非线性稳定项。在扩散主导的情况下，估计量与真实误差具有相同的收敛特性。讨论了第二种方法，其中使用 [20] 中提出的 Streamline Upwind Petrov Galerkin (SUPG) 估计器以后验方式推导出上限。数值例子研究了二维限制器的有效性指标和自适应网格细化。