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DC Field | Value | Language |
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dc.contributor.author | Shaw, S | - |
dc.contributor.author | Kruse, C | - |
dc.date.accessioned | 2014-03-06T11:46:13Z | - |
dc.date.available | 2014-03-06T11:46:13Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 36(1), B1 - B13, 2014 | en_US |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://epubs.siam.org/doi/abs/10.1137/130914589 | en |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/8120 | - |
dc.description | Copyright © by SIAM | en_US |
dc.description.abstract | In Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6685—6708 Werder et al. demonstrated that time discretizations of the heat equation by a temporally discontinuous Galerkin finite element method could be decoupled by diagonalising the temporal ‘Gram matrices’. In this article we propose a companion approach for the heat equation by using a continuous Galerkin time discretization. As a result, if piecewise polynomials of degree d are used as the trial functions in time and the spatial discretization produces systems of dimension M then, after decoupling, d systems of size M need to be solved rather than a single system of sizeMd. These decoupled systems require complex arithmetic, as did Werder et al.’s technique, but are amenable to parallel solution on modern multi-core architectures. We give numerical tests for temporal polynomial degrees up to six for three different model test problems, using both Galerkin and spectral element spatial discretizations, and show convergence and temporal superconvergence rates that accord with the bounds given by Aziz and Monk, Math. Comp. 52:186 (1989), pp. 255—274. We also interpret error as a function of computational time and see that our high order schemes may offer greater efficiency that the Crank-Nicolson method in terms of accuracy per unit of computational time—although in a multi-core world, with highly tuned iterative solvers, one has to be cautious with such claims. We close with a speculation on the application of these ideas to the Navier-Stokes equations for incompressible fluids. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | Continuous Galerkin finite element method | en_US |
dc.subject | Spectral element method | en_US |
dc.subject | Space-time finite elements | en_US |
dc.subject | High order methods | en_US |
dc.title | Time-decoupled high order continuous space-time finite element schemes for the heat equation | en_US |
dc.type | Article | en_US |
dc.identifier.doi | http://dx.doi.org/10.1137/130914589 | - |
pubs.organisational-data | /Brunel | - |
pubs.organisational-data | /Brunel/Brunel Active Staff | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths/Maths | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups/Brunel Institute of Computational Mathematics | - |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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