Hybridizable discontinuous galerkin method for strongly damped wave problem

Abstract

We introduce and analyze a hybridizable discontinuous Galerkin (HDG) approach for the strongly damped linear wave equation. In our investigation, we derive a priori error estimates to demonstrate the optimal convergence of the approximations for both the solution and its gradient. Further, with the help of the dual problem, we present a post-processed solution and analyze its convergence rate, which is of order for , where k is the degree of the polynomial. We also propose a fully discrete scheme, which is of . To validate our theoretical findings, we perform numerical experiments.