A Hybridisable Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion-Reaction Equations
Year: 2020
Author: Wei Pi, Yihui Han, Shiquan Zhang
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.090419.041219
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 455–484
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Convection-diffusion-reaction equation hybridisable discontinuous Galerkin method semi-discrete fully discrete error estimate.