Premium
Adaptive finite element method for an optimal control problem of Stokes flow with L 2 ‐norm state constraint
Author(s) -
Niu Haifeng,
Yuan Lei,
Yang Danping
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2572
Subject(s) - a priori and a posteriori , estimator , finite element method , norm (philosophy) , polygon mesh , mathematics , optimal control , mathematical optimization , constraint (computer aided design) , residual , stokes flow , flow (mathematics) , algorithm , geometry , physics , philosophy , statistics , epistemology , political science , law , thermodynamics
SUMMARY An adaptive finite element approximation for an optimal control problem of the Stokes flow with an L 2 ‐norm state constraint is proposed. To produce good adaptive meshes, the a posteriori error estimates are discussed. The equivalent residual‐type a posteriori error estimators of the H 1 ‐error of state and L 2 ‐error of control are given, which are suitable to carry out the adaptive multi‐mesh finite element approximation. Some numerical experiments are performed to illustrate the efficiency of the a posteriori estimators. Copyright © 2011 John Wiley & Sons, Ltd.