تقرير
A conservative Eulerian finite element method for transport and diffusion in moving domains
| العنوان: | A conservative Eulerian finite element method for transport and diffusion in moving domains |
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| المؤلفون: | Olshanskii, Maxim, von Wahl, Henry |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M12, 65M20, 65M60, 65M85 |
| الوصف: | The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld & Olshanskii [ESAIM: M2AN, 53(2): 585-614, 2019] of a solution extension to realise the Eulearian time-stepping scheme. However, a reformulation of the partial differential equation is suggested to derive a scheme which conserves the quantity under consideration exactly on the discrete level. For the spatial discretisation, the paper considers an unfitted finite element method. Ghost-penalty stabilisation is used to release the discrete solution extension and gives a scheme robust against arbitrary intersections between the mesh and geometry interface. The stability is analysed for both first- and second-order backward differentiation formula versions of the scheme. Several numerical examples in two and three spatial dimensions are included to illustrate the potential of this method. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.07130 |
| رقم الأكسشن: | edsarx.2404.07130 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |