TY - JOUR
T1 - A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs
AU - Yu , Yong
AU - Chen , Gang
AU - Pi , Liangya
AU - Zhang , Yangwen
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 144
EP - 175
PY - 2020
DA - 2020/10
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2019-0190
UR - https://global-sci.org/intro/article_detail/nmtma/18330.html
KW - HDG method, ensemble methods, parameterized convection diffusion PDEs, numerical analysis.
AB - <p style="text-align: justify;">A new second order time stepping ensemble hybridizable discontinuous
Galerkin method for parameterized convection diffusion PDEs with various initial
and boundary conditions, body forces, and time depending coefficients is developed.
For ensemble solutions in $L^∞$($0$, $T$; $L^2$($Ω$)), a superconvergent rate with respect to
the freedom degree of the globally coupled unknowns for all the polynomials of
degree $k$ ≥ $0$ is established. The results of numerical experiments are consistent
with the theoretical findings.</p>