Volume 14, Issue 1
A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 144-175.

Published online: 2020-10

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• Abstract

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.

• Keywords

HDG method, ensemble methods, parameterized convection diffusion PDEs, numerical analysis.

65M60

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@Article{NMTMA-14-144, author = {Yu , Yong and Chen , Gang and Pi , Liangya and Zhang , Yangwen}, title = {A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {14}, number = {1}, pages = {144--175}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0190}, url = {http://global-sci.org/intro/article_detail/nmtma/18330.html} }
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 -

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.

Yong Yu, Gang Chen, Liangya Pi & Yangwen Zhang. (2020). A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs. Numerical Mathematics: Theory, Methods and Applications. 14 (1). 144-175. doi:10.4208/nmtma.OA-2019-0190
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