论文标题
后验误差分析，用于近似时间分数次扩散问题
A posteriori error analysis for approximations of time-fractional subdiffusion problems
论文作者
论文摘要
在本文中，我们考虑了一个子扩散问题，其中分数衍生物通过L1方案或卷积正交近似。我们提出了对数值方案的新解释，这些方案导致后验错误估计。我们的方法基于数值方案的适当刻度表示，作为扰动的演化方程和进化方程的稳定性估计。 $ l^2（h）$和$ l^\ infty（h）$最佳顺序规范中的后验错误估计。广泛的数值实验表明了所考虑的方案的估计器的可靠性和最佳性，以及它们作为驱动自适应网格选择的误差指标定位了问题的奇异性。
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori error estimates. Our approach is based on appropriate pointwise representations of the numerical schemes as perturbed evolution equations and on stability estimates for the evolution equation. A posteriori error estimates in $L^2(H)$ and $L^\infty (H)$ norms of optimal order are derived. Extensive numerical experiments indicate the reliability and the optimality of the estimators for the schemes considered, as well as their efficiency as error indicators driving adaptive mesh selection locating singularities of the problem.
