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

TL;DR

This paper develops semi-discrete and fully discrete HDG methods for solving Burgers' equation in multiple dimensions, providing optimal error estimates and numerical validation of the proposed schemes.

Contribution

It introduces novel HDG discretization strategies for Burgers' equation with rigorous error analysis and numerical experiments demonstrating their effectiveness.

Findings

Optimal a priori error estimates derived.

Numerical experiments confirm theoretical accuracy.

Methods applicable in 2D and 3D settings.

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 \ (k \geq 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.