Adaptive finite element method for an optimal control problem of Stokes flow with  L  2 ‐norm state constraint | Zendy

Niu Haifeng | Zendy; Yuan Lei | Zendy; Yang Danping | Zendy

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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.

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