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khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory

Giani, Stefano ; Engström, Christian LU and Grubišić, Luka (2023) In Journal of Computational and Applied Mathematics 429.
Abstract

In this paper, we present an adaptive spectral projection based finite element method to numerically approximate the solution of the wave equation with memory. The adaptivity is not restricted to the mesh (hp-adaptivity), but it is also applied to the size of the computed spectrum (k-adaptivity). The meshes are refined using a residual based error estimator, while the size of the computed spectrum is adapted using the L2 norm of the error of the projected data. We show that the approach can be very efficient and accurate.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Automatic adaptivity, Discontinuous Galerkin method, Inverse Laplace transform, Spectral projection, Wave equation with delay
in
Journal of Computational and Applied Mathematics
volume
429
article number
115212
publisher
Elsevier
external identifiers
  • scopus:85151265664
ISSN
0377-0427
DOI
10.1016/j.cam.2023.115212
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2023 The Author(s)
id
745f3746-772a-4885-b202-552754775253
date added to LUP
2023-04-09 09:48:12
date last changed
2023-04-28 11:33:04
@article{745f3746-772a-4885-b202-552754775253,
  abstract     = {{<p>In this paper, we present an adaptive spectral projection based finite element method to numerically approximate the solution of the wave equation with memory. The adaptivity is not restricted to the mesh (hp-adaptivity), but it is also applied to the size of the computed spectrum (k-adaptivity). The meshes are refined using a residual based error estimator, while the size of the computed spectrum is adapted using the L<sup>2</sup> norm of the error of the projected data. We show that the approach can be very efficient and accurate.</p>}},
  author       = {{Giani, Stefano and Engström, Christian and Grubišić, Luka}},
  issn         = {{0377-0427}},
  keywords     = {{Automatic adaptivity; Discontinuous Galerkin method; Inverse Laplace transform; Spectral projection; Wave equation with delay}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Computational and Applied Mathematics}},
  title        = {{khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory}},
  url          = {{http://dx.doi.org/10.1016/j.cam.2023.115212}},
  doi          = {{10.1016/j.cam.2023.115212}},
  volume       = {{429}},
  year         = {{2023}},
}