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.

应用一致的 Argyris FEM 的主要缺点是一方面是费力的实施，另一方面是低收敛速度。如果没有使用适当的自适应网格，则只能实现由角奇异性引起的收敛速度（Blum 和 Rannacher，1980），远低于平滑函数的近似阶数。Argyris FEM 的精细逼近产生了高维线性系统，并且很长一段时间没有最优的预处理方案可用于非结构化网格。本文提出了数值基准，以确认来自 Carstensen 和 Hu (2021) 的分层 Argyris FEM 的自适应多级求解器实际上是高效且具有线性时间复杂度的。此外，在具有拐角奇异性和一般边界条件的实际相关基准中首次显示最佳收敛速度导致从计算角度恢复 Argyris 有限元。