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

Erik Burman (1) , Omar Duran (2, 3) , Alexandre Ern (2, 3) , Morgane Steins (4, 2, 3)

1 UCL London - Department of Mathematics
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
4 CEA - Commissariat à l'énergie atomique et aux énergies alternatives

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

Mots clés: Hybrid high-order methods; Error analysis; Wave equation; Elastodynamics

Domaines: Analyse numérique [math.NA]

Erik Burman, Omar Duran, Alexandre Ern, Morgane Steins. Convergence analysis of hybrid high-order methods for the wave equation. 2020. ⟨hal-02922720v1⟩