A conservative Eulerian finite element method for transport and diffusion in moving domains
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909659352268800 |
|---|---|
| author | Olshanskii, Maxim von Wahl, Henry |
| author_facet | Olshanskii, Maxim von Wahl, Henry |
| contents | The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld & Olshanskii [ESAIM: M2AN, 53(2): 585-614, 2019] of a solution extension to realise the Eulerian time-stepping scheme. However, a reformulation of the partial differential equation is suggested to derive a scheme which conserves the quantity under consideration exactly on the discrete level. For the spatial discretisation, the paper considers an unfitted finite element method. Ghost-penalty stabilisation is used to realise the discrete solution extension and gives a scheme robust against arbitrary intersections between the mesh and geometry interface. The stability is analysed for both first- and second-order backward differentiation formula versions of the scheme. Several numerical examples in two and three spatial dimensions are included to illustrate the potential of this method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07130 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A conservative Eulerian finite element method for transport and diffusion in moving domains Olshanskii, Maxim von Wahl, Henry Numerical Analysis 65M12, 65M60, 65M85 The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld & Olshanskii [ESAIM: M2AN, 53(2): 585-614, 2019] of a solution extension to realise the Eulerian time-stepping scheme. However, a reformulation of the partial differential equation is suggested to derive a scheme which conserves the quantity under consideration exactly on the discrete level. For the spatial discretisation, the paper considers an unfitted finite element method. Ghost-penalty stabilisation is used to realise the discrete solution extension and gives a scheme robust against arbitrary intersections between the mesh and geometry interface. The stability is analysed for both first- and second-order backward differentiation formula versions of the scheme. Several numerical examples in two and three spatial dimensions are included to illustrate the potential of this method. |
| title | A conservative Eulerian finite element method for transport and diffusion in moving domains |
| topic | Numerical Analysis 65M12, 65M60, 65M85 |
| url | https://arxiv.org/abs/2404.07130 |