On the hybridizable discontinuous Galerkin method and superconvergence analysis for the diffusive viscous wave equation

Abstract

This paper studies the hybridizable discontinuous Galerkin (HDG) method for solving the diffusive viscous wave equation. We provide a theoretical analysis of both the semi-discrete and fully-discrete schemes. Our results demonstrate that the displacement and the flux converge with an order of $m+1$ in the $L^2$ norm where m is the degree of polynomials. We also present a superconvergence analysis, indicating that the local post-processed variable converges with an order of $m+2$ in the $L^2$ norm. Finally, numerical tests verify our analysis.