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 - <p style="text-align: justify;">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.</p>