An initial-boundary value problem describing moisture transport in porous media: existence of strong solutions and an error estimate for a finite volume scheme
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914351418441728 |
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| author | Morimura, Akiko Aiki, Toyohiko |
| author_facet | Morimura, Akiko Aiki, Toyohiko |
| contents | We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by the finite volume method. In the proof of the error estimate, the Gagliardo--Nirenberg type inequality for the difference between a continuous function and a piecewise constant function plays an important role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An initial-boundary value problem describing moisture transport in porous media: existence of strong solutions and an error estimate for a finite volume scheme Morimura, Akiko Aiki, Toyohiko Analysis of PDEs Numerical Analysis 65M08, 35K59, 76S05 We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by the finite volume method. In the proof of the error estimate, the Gagliardo--Nirenberg type inequality for the difference between a continuous function and a piecewise constant function plays an important role. |
| title | An initial-boundary value problem describing moisture transport in porous media: existence of strong solutions and an error estimate for a finite volume scheme |
| topic | Analysis of PDEs Numerical Analysis 65M08, 35K59, 76S05 |
| url | https://arxiv.org/abs/2511.10378 |