title: High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling.
abstract: We revisit a method originally introduced by Werderet al.(in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimensionDand polynomials of degreerare used in time, the block system has dimension (r+ 1)Dand is usually regarded as being too large whenr> 1. Werderet al.found that the space-time coupling matrices are diagonalizable over [Formula: see text] forr ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors.International Journal for Numerical Methods in Engineeringpublished by John Wiley & Sons Ltd.
authors.affiliation: Center for Research in Scientific Computation, North Carolina State University Raleigh, NC 27695-8212, USA.
authors.forename: H T
authors.initials: HT
authors.lastname: Banks
authors.affiliation: Clinical Physics, Barts Health National Health Service Trust England.
authors.forename: Malcolm J
authors.initials: MJ
authors.lastname: Birch
authors.affiliation: Salisbury District Hospital England.
authors.forename: Mark P
authors.initials: MP
authors.lastname: Brewin
authors.affiliation: Blizard Institute, Barts and the London School of Medicine and Dentistry, Queen Mary, University of London England.
authors.forename: Stephen E
authors.initials: SE
authors.lastname: Greenwald
authors.affiliation: Center for Research in Scientific Computation, North Carolina State University Raleigh, NC 27695-8212, USA.
authors.forename: Shuhua
authors.initials: S
authors.lastname: Hu
authors.affiliation: Center for Research in Scientific Computation, North Carolina State University Raleigh, NC 27695-8212, USA.
authors.forename: Zackary R
authors.initials: ZR
authors.lastname: Kenz
authors.affiliation: BICOM, Brunel University Uxbridge, UB8 3PH, England.
authors.forename: Carola
authors.initials: C
authors.lastname: Kruse
authors.affiliation: BICOM, Brunel University Uxbridge, UB8 3PH, England.
authors.forename: Matthias
authors.initials: M
authors.lastname: Maischak
authors.affiliation: BICOM, Brunel University Uxbridge, UB8 3PH, England.
authors.forename: Simon
authors.initials: S
authors.lastname: Shaw
authors.affiliation: BICOM, Brunel University Uxbridge, UB8 3PH, England.
authors.forename: John R
authors.initials: JR
authors.lastname: Whiteman
keywords: discontinuous Galerkin finite element method; high order methods; space-time finite elements; spectral element method; viscoelasticity
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