East Asian J. Appl. Math., 10 (2020), pp. 455-484.
Published online: 2020-06
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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} }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.