In this paper, we consider a Lie splitting scheme for a nonlinear partial differential equation driven by a random time-dependent dispersion coefficient. Our main result is a uniform estimate of the error of the scheme when the time step goes to 0. Moreover, we prove that the scheme satisfies an asymptotic-preserving property. As an application, we study the order of convergence of the scheme when the dispersion coefficient approximates a (multi)fractional process.
Accepté le :
DOI : 10.1051/ps/2016023
Mots-clés : Nonlinear partial differential equations, splitting, stochastic partial differential equations, asymptotic-Preserving schemes, fractional and multifractional processes
@article{PS_2016__20__572_0,
author = {Duboscq, Romain and Marty, Renaud},
title = {Analysis of a splitting scheme for a class of random nonlinear partial differential equations},
journal = {ESAIM: Probability and Statistics},
pages = {572--589},
publisher = {EDP-Sciences},
volume = {20},
year = {2016},
doi = {10.1051/ps/2016023},
mrnumber = {3607207},
zbl = {1358.35168},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2016023/}
}
TY - JOUR AU - Duboscq, Romain AU - Marty, Renaud TI - Analysis of a splitting scheme for a class of random nonlinear partial differential equations JO - ESAIM: Probability and Statistics PY - 2016 SP - 572 EP - 589 VL - 20 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2016023/ DO - 10.1051/ps/2016023 LA - en ID - PS_2016__20__572_0 ER -
%0 Journal Article %A Duboscq, Romain %A Marty, Renaud %T Analysis of a splitting scheme for a class of random nonlinear partial differential equations %J ESAIM: Probability and Statistics %D 2016 %P 572-589 %V 20 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2016023/ %R 10.1051/ps/2016023 %G en %F PS_2016__20__572_0
Duboscq, Romain; Marty, Renaud. Analysis of a splitting scheme for a class of random nonlinear partial differential equations. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 572-589. doi : 10.1051/ps/2016023. http://archive.numdam.org/articles/10.1051/ps/2016023/
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