A space-time continuous and coercive formulation for the wave equation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918379047092224 |
|---|---|
| author | Bignardi, Paolo Moiola, Andrea |
| author_facet | Bignardi, Paolo Moiola, Andrea |
| contents | We propose a new space-time variational formulation for wave equation initial-boundary value problems. The key property is that the formulation is coercive (sign-definite) and continuous in a norm stronger than $H^1(Q)$, $Q$ being the space-time cylinder. Coercivity holds for constant-coefficient impedance cavity problems posed in star-shaped domains, and for a class of impedance-Dirichlet problems. The formulation is defined using simple Morawetz multipliers and its coercivity is proved with elementary analytical tools, following earlier work on the Helmholtz equation. The formulation can be stably discretised with any $H^2(Q)$-conforming discrete space, leading to quasi-optimal space-time Galerkin schemes. Several numerical experiments show the excellent properties of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07268 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A space-time continuous and coercive formulation for the wave equation Bignardi, Paolo Moiola, Andrea Numerical Analysis 35L05, 65M60, 65M15 We propose a new space-time variational formulation for wave equation initial-boundary value problems. The key property is that the formulation is coercive (sign-definite) and continuous in a norm stronger than $H^1(Q)$, $Q$ being the space-time cylinder. Coercivity holds for constant-coefficient impedance cavity problems posed in star-shaped domains, and for a class of impedance-Dirichlet problems. The formulation is defined using simple Morawetz multipliers and its coercivity is proved with elementary analytical tools, following earlier work on the Helmholtz equation. The formulation can be stably discretised with any $H^2(Q)$-conforming discrete space, leading to quasi-optimal space-time Galerkin schemes. Several numerical experiments show the excellent properties of the method. |
| title | A space-time continuous and coercive formulation for the wave equation |
| topic | Numerical Analysis 35L05, 65M60, 65M15 |
| url | https://arxiv.org/abs/2312.07268 |