Finite difference and finite element methods for partial differential equations on fractals
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| Format: | Artículo científico |
| Langue: | en |
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Universidad Industrial de Santander
2022
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| _version_ | 1876455315570950144 |
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| author | LUIS F. CONTRERAS H. |
| author_facet | LUIS F. CONTRERAS H. |
| contents | Finite difference and finite element methods for partial differential equations on fractals LUIS F. CONTRERAS H. JUAN GALVIS Física, Astronomía y Matemáticas Fractal diffusion Laplacian on a fractal Renormalization constant In this paper, we present numerical procedures to compute so-lutions of partial differential equations posed on fractals. In particular, weconsider the strong form of the equation using standard graph Laplacian ma-trices and also weak forms of the equation derived using standard length orarea measure on a discrete approximation of the fractal set. We then intro-duce a numerical procedure to normalize the obtained diffusions, that is, away to compute the renormalization constant needed in the definitions of theactual partial differential equation on the fractal set. A particular case thatis studied in detail is the solution of the Dirichlet problem in the Sierpinskitriangle. Other examples are also presented including a non-planar Hata tree. 2022 artículo científico 0120-419X https://www.redalyc.org/articulo.oa?id=327075143003 https://www.redalyc.org/journal/3270/327075143003/ https://www.redalyc.org/journal/3270/327075143003/html/ https://www.redalyc.org/journal/3270/327075143003/327075143003.epub https://www.redalyc.org/journal/3270/327075143003/movil 10.18273/revint.v40n2-2022003 en http://www.redalyc.org/revista.oa?id=3270 Revista Integración application/pdf Universidad Industrial de Santander Revista Integración (Colombia) Num.2 Vol.40 |
| format | Artículo científico |
| id | redalyc_327075143003 |
| institution | Redalyc |
| language | en |
| publishDate | 2022 |
| publisher | Universidad Industrial de Santander |
| spellingShingle | Finite difference and finite element methods for partial differential equations on fractals LUIS F. CONTRERAS H. Física, Astronomía y Matemáticas Fractal diffusion Laplacian on a fractal Renormalization constant Finite difference and finite element methods for partial differential equations on fractals LUIS F. CONTRERAS H. JUAN GALVIS Física, Astronomía y Matemáticas Fractal diffusion Laplacian on a fractal Renormalization constant In this paper, we present numerical procedures to compute so-lutions of partial differential equations posed on fractals. In particular, weconsider the strong form of the equation using standard graph Laplacian ma-trices and also weak forms of the equation derived using standard length orarea measure on a discrete approximation of the fractal set. We then intro-duce a numerical procedure to normalize the obtained diffusions, that is, away to compute the renormalization constant needed in the definitions of theactual partial differential equation on the fractal set. A particular case thatis studied in detail is the solution of the Dirichlet problem in the Sierpinskitriangle. Other examples are also presented including a non-planar Hata tree. 2022 artículo científico 0120-419X https://www.redalyc.org/articulo.oa?id=327075143003 https://www.redalyc.org/journal/3270/327075143003/ https://www.redalyc.org/journal/3270/327075143003/html/ https://www.redalyc.org/journal/3270/327075143003/327075143003.epub https://www.redalyc.org/journal/3270/327075143003/movil 10.18273/revint.v40n2-2022003 en http://www.redalyc.org/revista.oa?id=3270 Revista Integración application/pdf Universidad Industrial de Santander Revista Integración (Colombia) Num.2 Vol.40 |
| title | Finite difference and finite element methods for partial differential equations on fractals |
| topic | Física, Astronomía y Matemáticas Fractal diffusion Laplacian on a fractal Renormalization constant |
| url | https://www.redalyc.org/articulo.oa?id=327075143003 https://www.redalyc.org/journal/3270/327075143003/ https://www.redalyc.org/journal/3270/327075143003/html/ https://www.redalyc.org/journal/3270/327075143003/327075143003.epub https://www.redalyc.org/journal/3270/327075143003/movil |