Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions
Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions
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DOI：
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发表时间：
2011
影响因子：
1.1
通讯作者：
Xiaoming He;Tao Lin;Yanping Lin
中科院分区：
文献类型：
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作者：
Xiaoming He;Tao Lin;Yanping Lin
抽象的。本文建立了求解具有间断系数和非齐次跳跃条件的二阶椭圆边值问题的浸没有限元(IFE)函数。这些IFE函数可以在与界面无关的网格上形成。数值算例表明，这些IFE函数具有通常所采用的多项式的逼近能力。基于Galerkin公式的相关IFE方法可以看作是文献中为均匀跳跃条件而发展的IFE方法的自然推广，它们可以最优地求解具有非均匀通量跳跃条件的界面问题。
Abstract. This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.