Residual-based a posteriori error estimators for algebraic stabilizations

被引：0
|
作者：
Jha, Abhinav [1 ]
机构：
[1] Univ Stuttgart, Inst Appl Anal & Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
来源：
APPLIED MATHEMATICS LETTERS | 2024年 / 157卷
关键词：
Steady-state convection diffusion reaction equations; Algebraically stabilized finite element methods; A posteriori estimator; Adaptive grid refinement;
D O I：
10.1016/j.aml.2024.109192
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes (Jha, 2021) to the newly proposed algebraic stabilization schemes (John and Knobloch, 2022; Knobloch, 2023). Numerical simulations on adaptively refined grids are performed in two dimensions showing the higher efficiency of an algebraic stabilization with similar accuracy compared with an AFC scheme.
引用
收藏
页数：7
相关论文
共 50 条
  • [1] On a residual-based a posteriori error estimator for the total error
    Papez, Jan
    Strakos, Zdenek
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2018, 38 (03) : 1164 - 1184
  • [2] Some new residual-based a posteriori error estimators for the mortar finite element methods
    Feng Wang
    Xuejun Xu
    [J]. Numerische Mathematik, 2012, 120 : 543 - 571
  • [3] Some new residual-based a posteriori error estimators for the mortar finite element methods
    Wang, Feng
    Xu, Xuejun
    [J]. NUMERISCHE MATHEMATIK, 2012, 120 (03) : 543 - 571
  • [4] A note on the efficiency of residual-based a-posteriori error estimators for some mixed finite element methods
    Gatica, GN
    [J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2004, 17 : 218 - 233
  • [5] RANDOMIZED RESIDUAL-BASED ERROR ESTIMATORS FOR PARAMETRIZED EQUATIONS
    Smetana, Kathrin
    Zahm, Olivier
    Patera, Anthony T.
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2019, 41 (02): : A900 - A926
  • [6] On residual-based a posteriori error estimation in hp-FEM
    J.M. Melenk
    B.I. Wohlmuth
    [J]. Advances in Computational Mathematics, 2001, 15 : 311 - 331
  • [7] Residual-based a posteriori error estimation for stochastic magnetostatic problems
    Mac, D. H.
    Tang, Z.
    Clenet, S.
    Creuse, E.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 289 : 51 - 67
  • [8] On residual-based a posteriori error estimation in hp-FEM
    Melenk, JM
    Wohlmuth, BI
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2001, 15 (1-4) : 311 - 331
  • [9] REFINED FULLY EXPLICIT A POSTERIORI RESIDUAL-BASED ERROR CONTROL
    Carstensen, C.
    Merdon, C.
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (04) : 1709 - 1728
  • [10] Residual-based a posteriori error estimate for hypersingular equation on surfaces
    Carsten Carstensen
    M. Maischak
    D Praetorius
    E.P. Stephan
    [J]. Numerische Mathematik, 2004, 97 : 397 - 425
12345