论文标题
自适应最小二乘有限元方案的审查和计算比较
Review and computational comparison of adaptive least-squares finite element schemes
论文作者
论文摘要
最小二乘有限元方法的收敛分析导致了各种自适应网格重新策略：由内置的后验误差估算器或基于替代误差依据依次估计器和最佳数据近似算法的替代标记策略以及单独的标记策略所驱动的集体标记算法。本文回顾并讨论了可用的收敛结果。此外，在两个空间维度中，对一组二阶椭圆形偏微分方程的基准示例进行了经验研究。特别的兴趣是选择标记和改进参数以及给定数据的近似值。使用Platform Code Ocean上可用的作者软件包OCTAFEM可重现数值实验。
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit residual-based error estimator as well as a separate marking strategy based on the alternative error estimator and an optimal data approximation algorithm. This paper reviews and discusses available convergence results. In addition, all three strategies are investigated empirically for a set of benchmarks examples of second-order elliptic partial differential equations in two spatial dimensions. Particular interest is on the choice of the marking and refinement parameters and the approximation of the given data. The numerical experiments are reproducible using the author's software package octAFEM available on the platform Code Ocean.
