Convergence analysis of hybrid high-order methods for the wave equation (Q2031870)

The error estimates for the wave equation semi-discretized in space by the hybrid high-order (HHO) method are proved. The paper is organized as follows. Section 1 is an introduction. In Section 2, a brief overview of HHO methods for the discretization of a model diffusion problem and study the approximation properties of the HHO solution map are given. The acoustic wave equation in its second-order formulation, describe its semi-discretization in space using HHO methods, and perform the error analysis in the \(H^1\) and \(L^2\)-norms is presented in Section 3. For the acoustic wave equation in its first-order formulation, focusing on the \(H^1\)-norm error analysis the same is done in Section 4. In Section 5, the schemes are extended to elastodynamics and the time discretization by either Newmark or Runge-Kutta schemes are discussed. The numerical results with graphical illustrations are presented and analyzed in Section 6. Finally, some conclusions are given in Section 7.