Review and computational comparison of adaptive least-squares finite element schemes

被引:1
|
作者
Bringmann, Philipp [1 ]
机构
[1] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria
基金
奥地利科学基金会;
关键词
Least-squares finite element method; Adaptive mesh refinement; Alternative a posteriori error estimation; Separate marking; Data approximation; Numerical experiments; QUASI-OPTIMAL CONVERGENCE; MESH REFINEMENT; ERROR ESTIMATORS; LOCAL REFINEMENT; SEPARATE MARKING; OPTIMALITY; ALGORITHM; AXIOMS; FEM;
D O I
10.1016/j.camwa.2024.07.022
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页码:1 / 15
页数:15
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