论文标题
时间阵线A后验误差控制，用于时间分数抛物线方程的高阶离散
Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations
论文作者
论文摘要
考虑使用Caputo时间衍生物的时间折叠式抛物线方程。对于此类方程式，我们探索并进一步开发了[7]中提出的A-tosteriori误差估计和自适应时间阶梯的新方法。我们根据该理论改善了较早的阶梯算法，并在高阶方法的背景下特别解决了其稳定，有效的实现。所考虑的方法包括一种L1-2方法和任意秩序的连续搭配方法，在这种情况下，显示自适应的时间网格可在溶液奇异性的存在下产生最佳的收敛速率。
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We improve the earlier time stepping algorithm based on this theory, and specifically address its stable and efficient implementation in the context of high-order methods. The considered methods include an L1-2 method and continuous collocation methods of arbitrary order, for which adaptive temporal meshes are shown to yield optimal convergence rates in the presence of solution singularities.
