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A posteriori error estimates of stabilized finite volume method for the Stokes equations
Author(s) -
Zhang Tong,
Mu Lin,
Yuan JinYun
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3457
Subject(s) - mathematics , estimator , norm (philosophy) , residual , finite volume method , a priori and a posteriori , upper and lower bounds , gauss , stokes problem , finite element method , work (physics) , mathematical analysis , statistics , algorithm , mechanics , thermodynamics , physics , philosophy , epistemology , quantum mechanics , political science , law
In this work, the residual‐type posteriori error estimates of stabilized finite volume method are studied for the steady Stokes problem based on two local Gauss integrations. By using the residuals between the source term and numerical solutions, the computable global upper and local lower bounds for the errors of velocity in H 1 norm and pressure in L 2 norm are derived. Furthermore, a global upper bound of u − u h in L 2 ‐norm is also derived. Finally, some numerical experiments are provided to verify the performances of the established error estimators. Copyright © 2015 John Wiley & Sons, Ltd.