Error estimates for the patch bubble method for convection-dominated channel flow problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917427362660352 |
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| author | Bänsch, Eberhard Morin, Pedro Zocola, Itatí |
| author_facet | Bänsch, Eberhard Morin, Pedro Zocola, Itatí |
| contents | We present error estimates for the BMZ (Bubble Mesh Zoom) residual-free bubble method applied to a convection-diffusion equation in the convection-dominated regime. The method incorporates both element bubbles and residual-free bubbles supported on patches of two adjacent elements.
We focus on the case of a parallel flow in a square domain and derive error estimates in an energy norm that remain valid as diffusion becomes small. The theoretical findings are corroborated by numerical experiments, which also exhibit a competitive performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20025 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error estimates for the patch bubble method for convection-dominated channel flow problem Bänsch, Eberhard Morin, Pedro Zocola, Itatí Numerical Analysis 65M60 (Primary) 65N30, 65N12 (Secondary) We present error estimates for the BMZ (Bubble Mesh Zoom) residual-free bubble method applied to a convection-diffusion equation in the convection-dominated regime. The method incorporates both element bubbles and residual-free bubbles supported on patches of two adjacent elements. We focus on the case of a parallel flow in a square domain and derive error estimates in an energy norm that remain valid as diffusion becomes small. The theoretical findings are corroborated by numerical experiments, which also exhibit a competitive performance of the method. |
| title | Error estimates for the patch bubble method for convection-dominated channel flow problem |
| topic | Numerical Analysis 65M60 (Primary) 65N30, 65N12 (Secondary) |
| url | https://arxiv.org/abs/2604.20025 |