The collective marking strategy with alternative refinement-indicators in adaptive mesh-refining of least-squares finite element methods (LSFEMs) has recently been shown to lead to optimal convergence rates in Carstensen (2020). The proofs utilize explicit identities for the lowest-order Raviart–Thomas and the Crouzeix–Raviart finite elements. This paper generalizes those results to arbitrary polynomial degree and mixed boundary conditions with some novel arguments. The analysis is outlined for the Poisson equation in 3D with mixed boundary conditions.

中文翻译：

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具有最优速率的任意阶自适应最小二乘有限元方法的集体标记

最近在最小二乘有限元方法（LSFEM）的自适应网格细化中采用替代细化指标的集体标记策略已显示出可在Carstensen（2020）中实现最佳收敛速度。证明使用最低阶Raviart-Thomas和Crouzeix-Raviart有限元的显式标识。本文用一些新颖的论点将这些结果推广到任意多项式度和混合边界条件。概述了混合边界条件下的3D泊松方程。