论文标题
Argyris元素的最佳多层自适应FEM
Optimal multilevel adaptive FEM for the Argyris element
论文作者
论文摘要
适用于Argyris FEM的应用的主要缺点是一方面的劳动实施，另一方面是低收敛率。如果没有使用适当的自适应网格，则只能实现角落奇点引起的收敛速率[Blum and Rannacher，1980]，远低于平滑功能的近似顺序。与Argyris Fem的罚款近似可产生高维线性系统，并且长期以来不可用于非结构化网格的最佳预处理方案。本文介绍了数值基准，以确认[Carstensen and Hu，2021]的分层Argyris fem的自适应多级求解器实际上是高效且线性时间复杂性的。此外，从计算角度来看，在具有角度奇异性和一般边界条件的实际相关基准和一般边界条件的实际相关基准测试中的最佳收敛速率从计算角度出发。
The main drawback for the application of the conforming Argyris FEM is the labourious implementation on the one hand and the low convergence rates on the other. If no appropriate adaptive meshes are utilised, only the convergence rate caused by corner singularities [Blum and Rannacher, 1980], far below the approximation order for smooth functions, can be achieved. The fine approximation with the Argyris FEM produces high-dimensional linear systems and for a long time an optimal preconditioned scheme was not available for unstructured grids. This paper presents numerical benchmarks to confirm that the adaptive multilevel solver for the hierarchical Argyris FEM from [Carstensen and Hu, 2021] is in fact highly efficient and of linear time complexity. Moreover, the very first display of optimal convergence rates in practically relevant benchmarks with corner singularities and general boundary conditions leads to the rehabilitation of the Argyris finite element from the computational perspective.
