Goal-oriented error estimation for parameter-dependent nonlinear problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 705-728.

The main result of this paper gives a numerically efficient method to bound the error that is made when approximating the output of a nonlinear problem depending on an unknown parameter (described by a probability distribution). The class of nonlinear problems under consideration includes high-dimensional nonlinear problems with a nonlinear output function. A goal-oriented probabilistic bound is computed by considering two phases. An offline phase dedicated to the computation of a reduced model during which the full nonlinear problem needs to be solved only a small number of times. The second phase is an online phase which approximates the output. This approach is applied to a toy model and to a nonlinear partial differential equation, more precisely the Burgers equation with unknown initial condition given by two probabilistic parameters. The savings in computational cost are evaluated and presented.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2018003
Classification : 49Q12, 62F12, 65C20, 82C80
Mots clés : Goal-oriented, probabilistic error estimation, nonlinear problems, uncertainty quantification
Janon, Alexandre 1 ; Nodet, Maëlle 1 ; Prieur, Christophe 1 ; Prieur, Clémentine 1

1
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     title = {Goal-oriented error estimation for parameter-dependent nonlinear problems},
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Janon, Alexandre; Nodet, Maëlle; Prieur, Christophe; Prieur, Clémentine. Goal-oriented error estimation for parameter-dependent nonlinear problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 705-728. doi : 10.1051/m2an/2018003. http://www.numdam.org/articles/10.1051/m2an/2018003/

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