FINITE ELEMENT ERROR ANALYSIS OF ELLIPTIC PDES WITH RANDOM COEFFICIENTS AND ITS APPLICATION TO MULTILEVEL MONTE CARLO METHODS

被引:114
|
作者
Charrier, J. [1 ]
Scheichl, R. [2 ]
Teckentrup, A. L. [2 ]
机构
[1] Aix Marseille Univ, Ctr Math & Informat, F-13453 Marseille 13, France
[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
基金
英国工程与自然科学研究理事会;
关键词
PDEs with stochastic data; not uniformly elliptic or bounded; lack of full regularity; log-normal coefficients; truncated Karhunen-Loeve expansion; PARTIAL-DIFFERENTIAL-EQUATIONS;
D O I
10.1137/110853054
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a finite element approximation of elliptic partial differential equations with random coefficients. Such equations arise, for example, in uncertainty quantification in subsurface flow modeling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, have only very limited spatial regularity and lead to variational problems that lack uniform coercivity and boundedness with respect to the random parameter. In our analysis we overcome these challenges by a careful treatment of the model problem almost surely in the random parameter, which then enables us to prove uniform bounds on the finite element error in standard Bochner spaces. These new bounds can then be used to perform a rigorous analysis of the multilevel Monte Carlo method for these elliptic problems that lack full regularity and uniform coercivity and boundedness. To conclude, we give some numerical results that confirm the new bounds.
引用
收藏
页码:322 / 352
页数:31
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