Symplectic-mixed finite element approximation of linear acoustic wave equations
type: Item
instance of: scholarly article
title: Symplectic-mixed finite element approximation of linear acoustic wave equations
zbMATH Open document ID: 1331.65139
author: Robert C. Kirby
author: Thinh T. Kieu
published in: Numerische Mathematik
publication date: 2015-10-30T00:00:00Z
review text: The authors develop a finite element method for the linear acoustic wave equation \[ \rho p_{t} + \nabla u = f, \] \[ \kappa ^{-1}u_{t} + \nabla p = g, \] on the polyhedral domain by space variables \(\Omega \subset \mathbb R^{d}\) and finite time interval \([0,T]\) with the usual initial conditions and the boundary condition \( u \nu = 0\) on \(\partial \Omega\), where \( \nu \) is the unit outward normal to \( \Omega\). The obtained approximate scheme preserves the essential properties of the initial problem, especially the positive definite functional of energy. The stability of the method is proved imposing several conditions on the time and space steps and other parameters of the problem.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 6502658
zbMATH Keywords: linear acoustic wave equation
zbMATH Keywords: finite element method
zbMATH Keywords: stability
describes a project that uses: FEniCS
describes a project that uses: SyFi
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s00211-014-0667-4
OpenAlex ID: W2015247199
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DOI: 10.1007/S00211-014-0667-4
description: scientific article; zbMATH DE number 6502658