Semi-discrete and fully discrete HDG methods for Burgers' equation

This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two and three dimensions. In the spatial discretization, we use piecewise polynomials of degrees \begin{document}$ k \ (k \geq 1), k-1 $\end{document} and \begin{document}$ l \ (l = k-1; k) $\end{document} to approximate the scalar function, flux variable and the interface trace of scalar function, respectively. In the full discretization method, we apply a backward Euler scheme for the temporal discretization. Optimal a priori error estimates are derived. Numerical experiments are presented to support the theoretical results.