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A priori error estimation for the stochastic perturbation method

Xiang-Yu Wang, Song Cen, C.F. Li, D.R.J. Owen, Chenfeng Li Orcid Logo, Roger Owen Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 286, Pages: 1 - 21

Swansea University Authors: Chenfeng Li Orcid Logo, Roger Owen Orcid Logo

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DOI (Published version): 10.1016/j.cma.2014.11.044

Abstract

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 proba...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa21428
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first_indexed 2015-05-16T02:03:33Z
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spelling 2018-04-14T12:07:07.0305748 v2 21428 2015-05-15 A priori error estimation for the stochastic perturbation method 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 0303b9485caf6fbc8787397a5d926d1c 0000-0003-2471-0544 Roger Owen Roger Owen true false 2015-05-15 CIVL 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. Journal Article Computer Methods in Applied Mechanics and Engineering 286 1 21 0045-7825 1 4 2015 2015-04-01 10.1016/j.cma.2014.11.044 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2018-04-14T12:07:07.0305748 2015-05-15T11:20:03.3504812 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Xiang-Yu Wang 1 Song Cen 2 C.F. Li 3 D.R.J. Owen 4 Chenfeng Li 0000-0003-0441-211X 5 Roger Owen 0000-0003-2471-0544 6
title A priori error estimation for the stochastic perturbation method
spellingShingle A priori error estimation for the stochastic perturbation method
Chenfeng Li
Roger Owen
title_short A priori error estimation for the stochastic perturbation method
title_full A priori error estimation for the stochastic perturbation method
title_fullStr A priori error estimation for the stochastic perturbation method
title_full_unstemmed A priori error estimation for the stochastic perturbation method
title_sort A priori error estimation for the stochastic perturbation method
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
0303b9485caf6fbc8787397a5d926d1c
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
0303b9485caf6fbc8787397a5d926d1c_***_Roger Owen
author Chenfeng Li
Roger Owen
author2 Xiang-Yu Wang
Song Cen
C.F. Li
D.R.J. Owen
Chenfeng Li
Roger Owen
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 286
container_start_page 1
publishDate 2015
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2014.11.044
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 0
active_str 0
description 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.
published_date 2015-04-01T03:25:25Z
_version_ 1763750890909466624
score 11.012678

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