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.
机构:
Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USALouisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
Brenner, Susanne C.
Sung, Li-Yeng
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机构:
Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USALouisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
Sung, Li-Yeng
Tan, Zhiyu
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机构:
Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performan, Xiamen 361005, Fujian, Peoples R ChinaLouisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA