Semi-discrete and fully discrete HDG methods for Burgers' equation
Numerical Analysis
2021-02-02 v1 Numerical Analysis
Abstract
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 and 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.
Keywords
Cite
@article{arxiv.2102.00613,
title = {Semi-discrete and fully discrete HDG methods for Burgers' equation},
author = {Zimo Zhu and Gang Chen and Xiaoping Xie},
journal= {arXiv preprint arXiv:2102.00613},
year = {2021}
}