Convergence Analysis of Hybrid High-Order Methods for the Wave Equation

We prove error estimates for the wave equation semi-discretized in space by hybrid high-order (HHO) method. These lead to optimal convergence rates smooth solutions. consider first second-order formulation time, which we establish $${\varvec{H}}^1$$ and $${\varvec{L}}^2$$ -error estimates, then first-order formulation, estimates. For both formulations, semi-discrete HHO scheme has close links with hybridizable discontinuous Galerkin schemes from literature. Numerical experiments using either Newmark or diagonally-implicit Runge–Kutta time discretization illustrate theoretical findings show that proposed numerical can be used simulate accurately propagation of elastic waves heterogeneous media.