论文标题
随机搭配有限元元件的误差估计和适应性第二部分：多级近似
Error estimation and adaptivity for stochastic collocation finite elements Part II: multilevel approximation
论文作者
论文摘要
在这项工作中，召回了使用随机数据求解线性椭圆偏微分方程的多级自适应策略。该策略扩展了Guignard和Nobile在2018年引入的A后验误差估计框架（Siam J.Numer。Anal，56，3121---3143），以涵盖非携带参数系数依赖性的问题。策略的次优，但可靠且方便的实现涉及与公共有限元近似空间的脱钩PDE问题的近似。在这项工作的第一部分中介绍了使用这种单层策略获得的计算结果（Bespalov，Silvester和Xu，Arxiv：2109.07320）。本文讨论了使用单独定制网格的潜在更有效的多层近似策略获得的结果。用于生成数值结果的代码可在线获得。
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and Nobile in 2018 (SIAM J. Numer. Anal, 56, 3121--3143) to cover problems with a nonaffine parametric coefficient dependence. A suboptimal, but nonetheless reliable and convenient implementation of the strategy involves approximation of the decoupled PDE problems with a common finite element approximation space. Computational results obtained using such a single-level strategy are presented in part I of this work (Bespalov, Silvester and Xu, arXiv:2109.07320). Results obtained using a potentially more efficient multilevel approximation strategy, where meshes are individually tailored, are discussed herein. The codes used to generate the numerical results are available online.
