Composite finite elements for the approximation of PDEs on domains with complicated micro-structures
Composite finite elements for the approximation of PDEs on domains with complicated micro-structures
复制标题
DOI：
10.1007/s002110050248
复制
发表时间：
1997-02
影响因子：
2.1
通讯作者：
W. Hackbusch;S. Sauter
中科院分区：
文献类型：
--
作者：
W. Hackbusch;S. Sauter
通常，有限元空间的最小维度与感兴趣的物理对象的几何形状密切相关。这意味着有时从所需精度的角度来看，域中小型微观结构的分辨率需要不够精细的有限元网格。这一事实也限制了多重网格方法在实际情况中的应用，因为最粗网格应该解析物理对象的条件往往会导致最粗层次上的大量未知数。我们在这里提出了一种与物体形状无关的粗化有限元空间的策略。该技术可用于解决只有几个自由度的复杂域，并将多重网格方法有效地应用于具有复杂边界的域上的偏微分方程。在本文中，我们将证明这些广义有限元空间的近似性质。
Usually, the minimal dimension of a finite element space is closely related to the geometry of the physical object of interest. This means that sometimes the resolution of small micro-structures in the domain requires an inadequately fine finite element grid from the viewpoint of the desired accuracy. This fact limits also the application of multi-grid methods to practical situations because the condition that the coarsest grid should resolve the physical object often leads to a huge number of unknowns on the coarsest level. We present here a strategy for coarsening finite element spaces independently of the shape of the object. This technique can be used to resolve complicated domains with only few degrees of freedom and to apply multi-grid methods efficiently to PDEs on domains with complex boundary. In this paper we will prove the approximation property of these generalized FE spaces.