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Shape inverse problem for the two‐dimensional unsteady Stokes flow
Author(s) -
Yan Wenjing,
He Yaling,
Ma Yichen
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20454
Subject(s) - mathematics , differentiable function , inverse problem , nonlinear system , boundary value problem , stokes flow , flow (mathematics) , stokes problem , partial differential equation , mathematical analysis , divergence (linguistics) , gauss , inverse , partial derivative , transformation (genetics) , geometry , finite element method , linguistics , physics , philosophy , biochemistry , chemistry , quantum mechanics , gene , thermodynamics
In this article, the shape inverse problem for the two‐dimensional unsteady Stokes flow has been presented. We employ Piola transformation to bypass the divergence free condition for the flow and prove the differentiability of the solution to the initial boundary value problem. For the approximate solution of the ill‐posed and nonlinear problem, we propose a regularized Gauss‐Newton method. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010