khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory
(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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https://lup.lub.lu.se/record/745f3746-772a-4885-b202-552754775253
- author
- Giani, Stefano ; Engström, Christian LU and Grubišić, Luka
- organization
- publishing date
- 2023-09
- 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}}, }