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Title: High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling
Authors: Banks, HT
Birch, MJ
Brewin, MP
Greenwald, SE
Hu, S
Kenz, ZR
Kruse, C
Maischak, M
Shaw, S
Whiteman, JR
Keywords: Discontinuous Galerkin finite element method;Spectral element method;Space-time finite elements;High order methods;Viscoelasticity
Issue Date: 2014
Publisher: Wiley
Citation: International Journal for Numerical Methods in Engineering, 98(2), 131 - 156, 2014
Abstract: We revisit a method originally introduced by Werder et 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 dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over inline image for r ⩽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.
Description: Copyright @ 2014 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
ISSN: 0029-5981
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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