Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems
Author (s): Serafin, K.; Magnain, B.; Florentin, E.; Parés, N. and Díez, P.
Journal: International Journal for Numerical Methods in Engineering
Volume: 110, Issue 5
Pages: 440 – 466
Date: 2017
Abstract:
This work focuses on providing accurate low-cost approximations of stochastic finite elements simulations in the framework of linear elasticity. In [E. Florentin, P. Diez, Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems, Comput. Methods Appl. Mech. Engrg. 225-228 (2012) 116-127], an adaptive strategy has been introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU cost gain. Technical insight of these two topics are presented in details and numerical examples show the interest of these new developments.
Bibtex:
@article {NPM_PD:16,
Author = {Kevin Serafin and Benoit Magnain and Eric Florentin and N\'uria Par\'\es and Pedro D\'iez},
title = {Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems},
journal = {International Journal for Numerical Methods in Engineering},
volume = {110},
number = {5},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.5363},
doi = {10.1002/nme.5363},
pages = {440--466},
keywords = {reduced basis, adaptivity, stochastic modeling, goal-oriented error assessment.},
year = {2017},
note = {nme.5363},
}