English

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 k (k1),k1 k \ (k \geq 1), k-1 and l (l=k1;k) 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.

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}
}