%0 Journal Article
%T Weak truncation error estimates for elliptic PDES with lorgnormal coefficients
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ Invariant Preserving SOlvers (IPSO)
%+ Institut de Recherche Mathématique de Rennes (IRMAR)
%A Charrier, Julia
%A Debussche, Arnaud
%< avec comité de lecture
%@ 2194-0401
%J Stochastics and Partial Differential Equations: Analysis and Computations
%I Springer US
%V 1
%N 1
%P 63-93
%8 2013
%D 2013
%K uncertainty quanti cation
%K elliptic PDE with random coe cients
%K 76S05ve expansion
%K 65C20
%K 60H35
%K Karhunen-Lo è65N15
%K lognormal distribution
%K weak error estimate
%Z 65N15, 65C20, 60H35, 76S05
%Z Computer Science [cs]Journal articles
%X In this work, we are interested in the weak error committed on the solution of an elliptic partial di erential equation with a lognormal coe cient, resulting from the approximation of the lognormal coe cient through a Karhunen-Lo eve expansion. We wish to improve results of a previous work, in which Lp-estimates of the weak error are provided. Only small enough values of p (the corresponding values of p depend on the space dimension) could be considered and such bounds are not su cient to be applied to practical cases. Moreover, the optimality of this weak order (which turns out to be twice the strong order) has not been studied numerically. Therefore, the aim of this paper is double. First we improve drastically the weak error estimate by providing a bound of the C1-norm of the weak error. This requires regularity results in Holder spaces, with explicit bounds for the constants. We also consider much more general test functions in the de nition of the weak error. Finally, we show the optimality of the weak order and illustrate this weak convergence with numerical results.
%G English
%L hal-00831328
%U https://hal.science/hal-00831328
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%~ IRMAR
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%~ EC-MARSEILLE
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%~ UNAM
%~ TESTALAIN1
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%~ UR1-MATH-STIC
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%~ UR1-MATH-NUM
%~ INSTITUT-AGRO
%~ IRMAR-ANM
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