Spectral discretizations of the Darcy’s equations with non standard boundary conditions
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Universidad San Francisco de Quito
2018
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| _version_ | 1876488707895197696 |
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| author | J. M. Bernard |
| author_facet | J. M. Bernard |
| contents | Spectral discretizations of the Darcy’s equations with non standard boundary conditions J. M. Bernard Multidisciplinaria (Ciencias Naturales y Exactas) Darcy equations Spectral methods numerical results boundary conditions This paper is devoted to the approximation of a nonstandard Darcy problem, which modelizes the ow in porous media, by spectral methods: the pressure is assigned on a part of the boundary. We propose two variational formulations, as well as three spectral discretizations. The second discretization improves the approximation of the divergence-free condition, but the error estimate on the pressure is not optimal, while the third one leads to optimal error estimate with a divergence-free discrete solution, which is important for some applications. Next, their numerical analysis is performed in detail and we present some numerical experiments which conrm the interest of the third discretization. 2018 artículo científico 1390-5384 https://www.redalyc.org/articulo.oa?id=726180883002 en http://www.redalyc.org/revista.oa?id=7261 Avances en Ciencias e Ingenierías application/pdf Universidad San Francisco de Quito Avances en Ciencias e Ingenierías (Ecuador) Num.1 Vol.10 |
| format | Artículo científico |
| id | redalyc_726180883002 |
| institution | Redalyc |
| language | en |
| publishDate | 2018 |
| publisher | Universidad San Francisco de Quito |
| spellingShingle | Spectral discretizations of the Darcy’s equations with non standard boundary conditions J. M. Bernard Multidisciplinaria (Ciencias Naturales y Exactas) Darcy equations Spectral methods numerical results boundary conditions Spectral discretizations of the Darcy’s equations with non standard boundary conditions J. M. Bernard Multidisciplinaria (Ciencias Naturales y Exactas) Darcy equations Spectral methods numerical results boundary conditions This paper is devoted to the approximation of a nonstandard Darcy problem, which modelizes the ow in porous media, by spectral methods: the pressure is assigned on a part of the boundary. We propose two variational formulations, as well as three spectral discretizations. The second discretization improves the approximation of the divergence-free condition, but the error estimate on the pressure is not optimal, while the third one leads to optimal error estimate with a divergence-free discrete solution, which is important for some applications. Next, their numerical analysis is performed in detail and we present some numerical experiments which conrm the interest of the third discretization. 2018 artículo científico 1390-5384 https://www.redalyc.org/articulo.oa?id=726180883002 en http://www.redalyc.org/revista.oa?id=7261 Avances en Ciencias e Ingenierías application/pdf Universidad San Francisco de Quito Avances en Ciencias e Ingenierías (Ecuador) Num.1 Vol.10 |
| title | Spectral discretizations of the Darcy’s equations with non standard boundary conditions |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) Darcy equations Spectral methods numerical results boundary conditions |
| url | https://www.redalyc.org/articulo.oa?id=726180883002 |