TY - JOUR
T1 - An Adaptive Hybrid Spectral Method for Stochastic Helmholtz Problems
AU - Wang , Guanjie
AU - Liao , Qifeng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1007
EP - 1026
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0101
UR - https://global-sci.org/intro/article_detail/nmtma/16964.html
KW - Uncertainty quantification, generalized polynomial chaos, spectral elements, Helmholtz equations.
AB - <p style="text-align: justify;">The implementation of an adaptive hybrid spectral method for Helmholtz
equations with random parameters is addressed in this work. New error indicators
for generalized polynomial chaos for stochastic approximations and spectral element
methods for physical approximations are developed, and systematic adaptive strategies are proposed associated with these error indicators. Numerical results show
that these error indicators provide effective estimates for the approximation errors,
and the overall adaptive procedure results in efficient approximation method for the
stochastic Helmholtz equations.</p>