2021/02/01 by Zhu, Zimo, Chen, Gang, Xie, Xiaoping
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2102.00613
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 k (k ≥ 1), k-1 and l (l=k-1; k) 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.