Coupling of Boundary Element Methods and Finite Element Methods
Coupling of Boundary Element Methods and Finite Element Methods
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边界元法与有限元法的耦合
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发表时间：
2004
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通讯作者：
E. Stephan
中科院分区：
文献类型：
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作者：
E. Stephan
在椭圆边值问题的数值处理中，边界元法和有限元法的耦合得到了广泛的应用。通常，有限元法应用于有界子域，而边界元子域可以是无界的，但没有非均匀或非线性材料行为。这一章给出了一个概述的FE/BE耦合椭圆界面问题的数学重点。我们集中在对称耦合方法，因为它的普遍适用性，并给出了先验和后验误差估计。此外，我们解决实施方面，如适当的预处理适当的求解器的Galerkin方程。作为新的发展，我们考虑了最小二乘耦合方法与一阶系统在有限元域，并考虑原始和双重FE/BE耦合方法与Signorini接触条件的界面问题。除了标准公式，混合有限元公式也被考虑。在弹性力学中的应用进行了讨论。我们提出基本定理的证明，因为我们认为这些证明对于理解数学方面是必不可少的。我们还提出了说明性的数值例子，并提供了一个列表的参考文献。
保留字：
边界元;
有限元;
耦合;
后验误差估计;
快速求解器;
最小二乘法;
Signorini问题;
非线性弹性;
原-对偶混合耦合法
For the numerical treatment of elliptic boundary value problems, the coupling of boundary element methods and finite element methods is widely used. Usually, the FEM is applied in a bounded subdomain, whereas the BEM subdomain may be unbounded, but without inhomogeneous or nonlinear material behavior. This chapter gives a survey of FE/BE coupling for elliptic interface problems with emphasis on mathematics. We concentrate on the symmetric coupling method because of its general applicability and give a priori and a posteriori error estimates. Further, we address implementational aspects such as suitable preconditioning for appropriate solvers of the Galerkin equations. As new developments, we consider a least squares coupling method with first-order systems in the FEM domain and consider both primal and dual FE/BE coupling methods for interface problems with Signorini contact condition. Besides standard formulations, mixed FEM formulations are also considered. Applications in elasticity are discussed. We present proofs of essential theorems because we feel that these proofs are essential for understanding the mathematical aspects. We also present illustrative numerical examples and provide a list of references to the current literature.
Keywords:
boundary elements;
finite elements;
coupling;
a posteriori error estimates;
fast solvers;
least squares methods;
Signorini problems;
nonlinear elasticity;
primal- and dual-mixed coupling methods