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.
翻译:在这项工作中回顾了解决线性椭圆部分差异方程式的多层次适应性完善战略,并附有随机数据。该战略扩展了Guignard和Nobile在2018年推出的事后误差估计框架(SIAM J.Numer.Anal, 56, 3121-3143),以涵盖非按成因参数系数依赖性的问题。本战略执行不理想,但可靠和方便,涉及将脱钩的PDE问题与共同的有限元素近似空间相近。这项工作第一部分介绍了使用这种单级战略取得的计算结果(Bespalov, Silvester和Xu, arXiv:219.07320)。本文讨论了利用可能更加有效的多层次近似战略取得的成果,在这些战略中,Memes是单独定制的。用于产生数字结果的代码可在网上查阅。