Convergence in the incompressible limit of the corner singularities
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913496003772416 |
|---|---|
| author | Choi, Hyung Jun Kim, Seonghak Koh, Youngwoo |
| author_facet | Choi, Hyung Jun Kim, Seonghak Koh, Youngwoo |
| contents | In this paper, we treat the corner singularity expansion and its convergence result regarding the penalized system obtained by eliminating the pressure variable in the Stokes problem of incompressible flow. The penalized problem is a kind of the Lamé system, so we first discuss the corner singularity theory of the Lamé system with inhomogeneous Dirichlet boundary condition on a non-convex polygon. Considering the inhomogeneous condition, we show the decomposition of its solution, composed of singular parts and a smoother remainder near a re-entrant corner, and furthermore, we provide the explicit formulae of coefficients in singular parts. In particular, these formulae can be used in the development of highly accurate numerical scheme. In addition, we formulate coefficients in singular parts regarding the Stokes equations with inhomogeneous boundary condition and non-divergence-free property of velocity field, and thus we show the convergence results of coefficients in singular parts and remainder regarding the concerned penalized problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence in the incompressible limit of the corner singularities Choi, Hyung Jun Kim, Seonghak Koh, Youngwoo Analysis of PDEs 35A21, 76D03 In this paper, we treat the corner singularity expansion and its convergence result regarding the penalized system obtained by eliminating the pressure variable in the Stokes problem of incompressible flow. The penalized problem is a kind of the Lamé system, so we first discuss the corner singularity theory of the Lamé system with inhomogeneous Dirichlet boundary condition on a non-convex polygon. Considering the inhomogeneous condition, we show the decomposition of its solution, composed of singular parts and a smoother remainder near a re-entrant corner, and furthermore, we provide the explicit formulae of coefficients in singular parts. In particular, these formulae can be used in the development of highly accurate numerical scheme. In addition, we formulate coefficients in singular parts regarding the Stokes equations with inhomogeneous boundary condition and non-divergence-free property of velocity field, and thus we show the convergence results of coefficients in singular parts and remainder regarding the concerned penalized problem. |
| title | Convergence in the incompressible limit of the corner singularities |
| topic | Analysis of PDEs 35A21, 76D03 |
| url | https://arxiv.org/abs/2409.06602 |