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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ k \ (k \geq 1), k-1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ l \ (l = k-1; k) $\end{document}</tex-math></inline-formula> 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.</p>