论文标题
对流扩散方程AFC方案的基于残差的后验误差估计器
A Residual Based A Posteriori Error Estimators for AFC Schemes for Convection-Diffusion Equations
论文作者
论文摘要
在这项工作中，我们为代数通量校正（AFC）方案提出了基于残差的后验误差估计器。对于限制器的一般选择，为能量规范的误差而得出了全局上限，该限制定义了非线性稳定项。在扩散为主导的方案中，估计器具有与真实误差相同的收敛属性。讨论了第二种方法，其中使用流线上的petrov galerkin（supg）估计量以\ cite {jn13}提出的流线向后降低了上限。数值示例研究了两个限制器在两个维度上的效率指数和自适应网格细化。
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 \cite{JN13}. Numerical examples study the effectivity index and the adaptive grid refinement for two limiters in two dimensions.
