A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution of a boundary value problem is approximated for various levels of uniform h and p refinements.
翻译:在 2D 矩形上执行简单的 MATLAB 级形函数的简单 MATLAB 功能可以下载。全球形状函数根据它们所属的节点、边缘或元素的指数,按一个多位度排序。对于统一的精细,等级结构可以有效地组合质量和坚硬度矩阵。边界值问题的解决方案可以大致用于各种水平的统一 h 和细化 。