A Study on Mixed Finite Element Formulations Applied to Diffusion Problems
A Study on Mixed Finite Element Formulations Applied to Diffusion Problems
复制标题
应用于扩散问题的混合有限元公式研究
DOI：
10.1002/pamm.201410230
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
amd Steinmann
中科院分区：
文献类型：
--
作者：
Kaessmair;Javili;amd Steinmann
这篇文章的目的是研究各种混合有限元格式应用于经典和非经典扩散问题。Fickean扩散被认为是使用三场公式，其中浓度梯度和扩散通量被另外选择为独立变量。进一步讨论了由Cahn-Hilliard方程给出的非经典扩散模型，其中采用混合有限元将四阶偏微分方程转化为两个二阶偏微分方程.一个惩罚的版本的一个混合制定的基础第二梯度模型是由特定的微观模型。另一种方法是经典的二阶分裂方法。（© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
The objective of this contribution is to study various mixed finite element schemes applied to classical and non‐classical diffusion problems. The Fickean diffusion is considered using a three‐field formulation where the concentration gradient and the diffusive flux are additionally chosen as independent variables. Furthermore, the non‐classical diffusion model given by the Cahn–Hilliard equation is discussed where mixed finite elements are used to cast the fourth‐order PDE into two second‐order PDEs. A penalized version of a mixed formulation for the underlying second gradient model is given by specific micromorphic models. Another approach is a classical second order splitting method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)