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A priori error estimation for the stochastic perturbation method

机译：随机摄动法的先验误差估计

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摘要

The perturbation method has been among the most popular stochastic finite element methods due to its simplicity and efficiency. The error estimation for the perturbation method is well established for deterministic problems, but until now there has not been an error estimation developed in the probabilistic context. This paper presents a priori error estimation for the perturbation method in solving stochastic partial differential equations. The physical problems investigated here come from linear elasticity of heterogeneous materials, where the material parameters are represented by stochastic fields. After applying the finite element discretization to the physical problem, a stochastic linear algebraic equation system is formed with a random matrix on the left hand side. Such systems have been efficiently solved by using the stochastic perturbation approach, without knowing how accurate/inaccurate the perturbation solution is. In this paper, we propose a priori error estimation to directly link the error of the solution vector with the variation of the source stochastic field. A group of examples are presented to demonstrate the effectiveness of the proposed error estimation. (C) 2014 Elsevier B.V. All rights reserved.
机译：摄动法由于其简单性和效率而成为最流行的随机有限元方法之一。对于确定性问题，已经很好地建立了扰动方法的误差估计，但是到目前为止，在概率环境中还没有开发出误差估计。本文提出了一种求解随机偏微分方程的摄动方法的先验误差估计。此处研究的物理问题来自异质材料的线性弹性，其中材料参数由随机场表示。在将有限元离散化应用于物理问题之后，形成了一个随机线性代数方程组，该系统在左侧具有一个随机矩阵。通过使用随机扰动方法已经有效地解决了这样的系统，而不知道扰动解的精确度/不准确度。在本文中，我们提出了一种先验误差估计，以直接将解向量的误差与源随机场的变化联系起来。给出了一组示例，以证明所提出的误差估计的有效性。 （C）2014 Elsevier B.V.保留所有权利。

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  • 作者

    Wang Xiang-Yu; Cen Song; Li C. F.; Owen D. R. J.;

  • 作者单位

    Tsinghua Univ, Sch Aerosp Engn, Dept Engn Mech, Beijing 100084, Peoples R China|Swansea Univ, Coll Engn, Zienkiewicz Ctr Computat Engn, Swansea SA2 8PP, W Glam, Wales;

    Tsinghua Univ, Sch Aerosp Engn, Dept Engn Mech, Beijing 100084, Peoples R China|Tsinghua Univ, Sch Aerosp Engn, Ctr High Performance Comp, Beijing 100084, Peoples R China|Tsinghua Univ, Sch Aerosp Engn, Key Lab Appl Mech, Beijing 100084, Peoples R China;

    Swansea Univ, Coll Engn, Zienkiewicz Ctr Computat Engn, Swansea SA2 8PP, W Glam, Wales|Swansea Univ, Energy Safety Res Inst, Coll Engn, Swansea SA2 8PP, W Glam, Wales;

    Swansea Univ, Coll Engn, Zienkiewicz Ctr Computat Engn, Swansea SA2 8PP, W Glam, Wales;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Error estimation; Stochastic finite element methods; The perturbation method;

    机译：误差估计随机有限元摄动法;

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