Advances in Discretization Methods - Discontinuities, Virtual Elements, Fictitious Domain Methods
Advances in Discretization Methods - Discontinuities, Virtual Elements, Fictitious Domain Methods
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离散化方法的进展 - 不连续性、虚拟元素、虚拟域方法
DOI：
10.1007/978-3-319-41246-7_9
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Collis J
中科院分区：
文献类型：
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作者：
Collis J
在这篇文章中，我们考虑的应用程序的间断Galerkin有限元方法，定义在凝聚网格组成的一般多面体元素，数值逼近的偏微分方程问题的复杂几何形状。在这里，我们假设，底层的计算域可以准确地表示由一个几何形状符合细网格，然后构建所得到的粗网格的基础上采用标准的图形分割算法。为了提高计算数值近似的准确性，我们考虑在自动网格细化策略中发展面向目标的自适应技术。在这种情况下，标记为细化的元素通过局部构造更细的团聚体进行细分;如果需要进一步解析底层的细网格，则还将进行自适应细化。作为这些技术的应用的一个例子，我们考虑的线性弹性方程的数值逼近均匀各向同性材料。特别是，所提出的自适应细化算法的性能进行了研究（缩放）的有效杨氏模量的一段骨小梁的计算。
In this article we consider the application of discontinuous Galerkin finite element methods, defined on agglomerated meshes consisting of general polytopic elements, to the numerical approximation of partial differential equation problems posed on complicated geometries. Here, we assume that the underlying computational domain may be accurately represented by a geometry-conforming fine mesh; the resulting coarse mesh is then constructed based on employing standard graph partitioning algorithms. To improve the accuracy of the computed numerical approximation, we consider the development of goal-oriented adaptation techniques within an automatic mesh refinement strategy. In this setting, elements marked for refinement are subdivided by locally constructing finer agglomerates; should further resolution of the underlying fine meshbe required, then adaptive refinement ofwill also be undertaken. As an example of the application of these techniques, we consider the numerical approximation of the linear elasticity equations for a homogeneous isotropic material. In particular, the performance of the proposed adaptive refinement algorithm is studied for the computation of the (scaled) effective Young’s modulus of a section of trabecular bone.