Convergence analysis of hybrid high-order methods for the wave equation
type: Item
instance of: scholarly article
title: Convergence analysis of hybrid high-order methods for the wave equation
zbMATH Open document ID: 1480.65248
author: Erik Burman
author: Omar Durán
author: Alexandre Ern
author: Morgane Steins
published in: Journal of Scientific Computing
publication date: 2021-06-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 7358940
zbMATH Keywords: hybrid high-order methods
zbMATH Keywords: error analysis
zbMATH Keywords: wave equation
zbMATH Keywords: elastodynamics
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: s10915-021-01492-1
OpenAlex ID: W3081875828
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DOI: 10.1007/S10915-021-01492-1
description: scientific article; zbMATH DE number 7358940