Book Review: Leszek Demkowicz, Computing with hp‐adaptive finite elements, Volume 1, One and two dimensional elliptic and Maxwell problems
Book Review: Leszek Demkowicz, Computing with hp‐adaptive finite elements, Volume 1, One and two dimensional elliptic and Maxwell problems
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书评：Leszek Demkowicz，使用 hp 自适应有限元进行计算，第 1 卷，一维和二维椭圆和麦克斯韦问题
DOI：
10.1002/zamm.200790013
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发表时间：
2007
影响因子：
2.3
通讯作者：
A. Düster
中科院分区：
文献类型：
--
作者：
A. Düster
第一部分讨论一维hp自适应有限元。章1定义了一维模型椭圆问题和基本符号。章2回顾Galerkin方法。1Dhp有限元法在第一章中解释。3，包括创建具有可变单元大小和多项式次数的有限元近似所需的成分。本书附带的一维hp-code在第二章有解释。4，其中讨论了数据结构，图形和元素例程等基础知识。网格细化，无论是在h和p的介绍在第章。5中，引入了h-加细延拓算子和基于投影的插值的概念.接下来，在第二章中介绍了一维问题的全自动hp自适应程序。6.第一部分以第一章结束。第二部分讨论二维椭圆问题，第三部分讨论椭圆问题，第四部分讨论椭圆问题，第五部分讨论椭圆问题，第六部分讨论椭圆问题。介绍顺序与第一部分相似。在第二章中给出了一个二维椭圆边值问题。8，Sobolev空间在多维背景下讨论的第一章。9.章10介绍了HP有限元的基本原理，在第10章中，11解释了随书提供的2D hp代码。由于几何描述的高阶元素是至关重要的，第章。12致力于几何建模和网格生成。h-加密网格上的hp-FEM及其自动hp-adaptation
Part I deals withhp-adaptive finite elements in 1D. Chap. 1 defines the 1D model elliptic problem and basic notation. Chap. 2 recalls the Galerkin method. The 1Dhpfinite element method is explained in Chap. 3, including the ingredients required to create a finite element approximation with variable element size and polynomial degree. The one-dimensional hp-code which comes with the book is explained in Chap. 4, where fundamentals like data structure, graphics, and element routines are discussed. Mesh refinements, both in h and p are presented in Chap. 5, where the concepts of h-refinement extension operators and projection-based interpolation are introduced. Next, the fully automatic hp-adaptive procedure for the 1D problem is presented in Chap. 6. Part I ends with Chap. 7, discussing wave propagation problems and extending the hp-adaptive procedure to the solution of a vibrating elastic bar.Part II is devoted to two-dimensional elliptic problems. The order of presentation is similar to that in Part I. After the formulation of a 2D elliptic boundary value problem in Chap. 8, Sobolev spaces in the multidimensional context are discussed in Chap. 9. Chap. 10 presents the fundamentals of hp finite elements and in Chap. 11 the 2D hp code which comes with the book is explained. Since the geometric description of high order elements is crucial, Chap. 12 is devoted to geometric modelling and mesh generation. The hp-FEM on h-refined meshes and automatic hp-adaptivity in