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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; Grubišić, Luka

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


Authors

Christian Engström

Luka Grubišić



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.

Citation

Giani, S., Engström, C., & Grubišić, L. (2023). khp-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory. Journal of Computational and Applied Mathematics, 429, Article 115212. https://doi.org/10.1016/j.cam.2023.115212

Journal Article Type Article
Acceptance Date Mar 7, 2023
Online Publication Date Mar 31, 2023
Publication Date 2023-09
Deposit Date Mar 9, 2023
Publicly Available Date Mar 28, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Electronic ISSN 1879-1778
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 429
Article Number 115212
DOI https://doi.org/10.1016/j.cam.2023.115212

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