Volume 10, Issue 3
A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations

East Asian J. Appl. Math., 10 (2020), pp. 455-484.

Published online: 2020-06

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• Abstract

A hybridisable discontinuous Galerkin (HDG) discretisation of time-dependent linear convection-diffusion-reaction equations is considered. For the space discretisation, the HDG method uses piecewise polynomials of degrees $k$ ≥ 0 to approximate potential $u$ and its trace on the inter-element boundaries, and the flux is approximated by piecewise polynomials of degree max{$k$ − 1, 0}, $k$ ≥ 0. In the fully discrete scheme, the time derivative is approximated by the backward Euler difference. Error estimates obtained for semi-discrete and fully discrete schemes show that the HDG method converges uniformly with respect to the equation coefficients. Numerical examples confirm the theoretical results.

• Keywords

Convection-diffusion-reaction equation, hybridisable discontinuous Galerkin method, semi-discrete, fully discrete, error estimate.

65M10, 78A48

1335751459@qq.com (Yihui Han)

guquan811119@163.com (Shiquan Zhang)

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@Article{EAJAM-10-455, author = {Wei and Pi and and 7883 and and Wei Pi and Yihui and Han and 1335751459@qq.com and 7884 and and Yihui Han and Shiquan and Zhang and guquan811119@163.com and 7885 and and Shiquan Zhang}, title = {A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {455--484}, abstract = {

A hybridisable discontinuous Galerkin (HDG) discretisation of time-dependent linear convection-diffusion-reaction equations is considered. For the space discretisation, the HDG method uses piecewise polynomials of degrees $k$ ≥ 0 to approximate potential $u$ and its trace on the inter-element boundaries, and the flux is approximated by piecewise polynomials of degree max{$k$ − 1, 0}, $k$ ≥ 0. In the fully discrete scheme, the time derivative is approximated by the backward Euler difference. Error estimates obtained for semi-discrete and fully discrete schemes show that the HDG method converges uniformly with respect to the equation coefficients. Numerical examples confirm the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090419.041219}, url = {http://global-sci.org/intro/article_detail/eajam/16977.html} }
TY - JOUR T1 - A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations AU - Pi , Wei AU - Han , Yihui AU - Zhang , Shiquan JO - East Asian Journal on Applied Mathematics VL - 3 SP - 455 EP - 484 PY - 2020 DA - 2020/06 SN - 10 DO - http://doi.org/10.4208/eajam.090419.041219 UR - https://global-sci.org/intro/article_detail/eajam/16977.html KW - Convection-diffusion-reaction equation, hybridisable discontinuous Galerkin method, semi-discrete, fully discrete, error estimate. AB -

A hybridisable discontinuous Galerkin (HDG) discretisation of time-dependent linear convection-diffusion-reaction equations is considered. For the space discretisation, the HDG method uses piecewise polynomials of degrees $k$ ≥ 0 to approximate potential $u$ and its trace on the inter-element boundaries, and the flux is approximated by piecewise polynomials of degree max{$k$ − 1, 0}, $k$ ≥ 0. In the fully discrete scheme, the time derivative is approximated by the backward Euler difference. Error estimates obtained for semi-discrete and fully discrete schemes show that the HDG method converges uniformly with respect to the equation coefficients. Numerical examples confirm the theoretical results.

Wei Pi, Yihui Han & Shiquan Zhang. (2020). A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations. East Asian Journal on Applied Mathematics. 10 (3). 455-484. doi:10.4208/eajam.090419.041219
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