Експоненціальна заміна у методі скінченних елементів для рівнянь адвекції-дифузії
A mathematical model of drug distribution in the artery wall during catheter treatment ofatherosclerosis, which is presented as initial-boundary value problem for a system of twodifferential equations, is formulated. During the first numerical experiment it was found that directapplication of the fi...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2018
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| Schlagworte: | |
| Online Zugang: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/47 |
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| Назва журналу: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Zusammenfassung: | A mathematical model of drug distribution in the artery wall during catheter treatment ofatherosclerosis, which is presented as initial-boundary value problem for a system of twodifferential equations, is formulated. During the first numerical experiment it was found that directapplication of the finite element method with standard linear and quadratic basis functions leadsto a loss of stability of the solution. This is due to the specifics of the input parameters of theproblem, in fact a significant advantage over advection coefficients of diffusion coefficients. Thedrawback is overcome by using approximations based on exponential replacement in problemformulation that leads to a loss of advection term and after by using reverse replacement insidefinite element method. Results of computational experiments for one-dimensional spatial variablesfor stationary problems are demonstrated. |
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