کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6925577 | 866720 | 2016 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The bulk-surface finite element method for reaction-diffusion systems on stationary volumes
ترجمه فارسی عنوان
روش عدسی محدود برای سطوح سطحی برای سیستم های واکنش-انتشار در حجم های ثابت
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کلمات کلیدی
معادلات دیفرانسیل واکنش سطحی سطح، عناصر محدود سطحی سطح، بی ثباتی رانده شده توسط نفوذ، شکل گیری الگو،
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
In this work we present the bulk-surface finite element method (BSFEM) for solving coupled systems of bulk-surface reaction-diffusion equations (BSRDEs) on stationary volumes. Such systems of coupled bulk-surface partial differential equations arise naturally in biological applications and fluid dynamics, for example, in modelling of cellular dynamics in cell motility and transport and diffusion of surfactants in two phase flows. In this proposed framework, we define the surface triangulation as a collection of the faces of the elements of the bulk triangulation whose vertices lie on the surface. This implies that the surface triangulation is the trace of the bulk triangulation. As a result, we construct two finite element spaces for the interior and surface respectively. To discretise in space we use piecewise bilinear elements and the implicit second order fractional-step θ scheme is employed to discretise in time. Furthermore, we use the Newton method to treat the nonlinearities. The BSFEM applied to a coupled system of BSRDEs reveals interesting patterning behaviour. For a set of appropriate model parameter values, the surface reaction-diffusion system is not able to generate patterns everywhere in the bulk except for a small region close to the surface while the bulk reaction-diffusion system is able to induce patterning almost everywhere. Numerical experiments are presented to reveal such patterning processes associated with reaction-diffusion theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Elements in Analysis and Design - Volume 108, January 2016, Pages 9-21
Journal: Finite Elements in Analysis and Design - Volume 108, January 2016, Pages 9-21
نویسندگان
Anotida Madzvamuse, Andy H.W. Chung,