Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908396180996096 |
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| author | Ferrari, Matteo Perugia, Ilaria Zampa, Enrico |
| author_facet | Ferrari, Matteo Perugia, Ilaria Zampa, Enrico |
| contents | In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation Ferrari, Matteo Perugia, Ilaria Zampa, Enrico Numerical Analysis 65M60, 65N12 In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We analyze the method, showing its stability without imposing any restrictions on the mesh size or time step, and proving quasi-optimal convergence for any choice of space-time tensor product discrete spaces that satisfies standard approximation assumptions. Numerical examples are provided to support the theoretical findings. |
| title | Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation |
| topic | Numerical Analysis 65M60, 65N12 |
| url | https://arxiv.org/abs/2506.05886 |