THE "EXTERIOR APPROACH" TO SOLVE THE INVERSE OBSTACLE PROBLEM FOR THE STOKES SYSTEM

被引：19

作者：

Bourgeois, Laurent ^{[1
]}

Darde, Jeremi ^{[2
]}

机构：

[1] ENSTA ParisTech, Lab POEMS, F-91762 Palaiseau, France

[2] Univ Toulouse, Inst Math, F-31062 Toulouse 9, France

来源：

INVERSE PROBLEMS AND IMAGING | 2014年 / 8卷 / 01期

关键词：

Stokes system; level set method; quasi-reversibility method; finite element method; inverse obstacle problem; QUASI-REVERSIBILITY METHOD; IDENTIFICATION; FORMULATION; COEFFICIENT; FLUID;

D O I：

10.3934/ipi.2014.8.23

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We apply an "exterior approach" based on the coupling of a method of quasi-reversibility and of a level set method in order to recover a fixed obstacle immersed in a Stokes flow from boundary measurements. Concerning the method of quasi-reversibility, two new mixed formulations are introduced in order to solve the ill-posed Cauchy problems for the Stokes system by using some classical conforming finite elements. We provide some proofs for the convergence of the quasi-reversibility methods on the one hand and of the level set method on the other hand. Some numerical experiments in 2D show the efficiency of the two mixed formulations and of the exterior approach based on one of them.

引用

页码：23 / 51

页数：29

共 35 条

[1] Identification of immersed obstacles via boundary measurements [J].

Alvarez, C ;

Conca, C ;

Friz, L ;

Kavian, O ;

Ortega, JH .

INVERSE PROBLEMS, 2005, 21 (05) :1531-1552

[2] On the identification of a rigid body immersed in a fluid: A numerical approach [J].

Alvarez, Catalina ;

Conca, Carlos ;

Lecaros, Rodrigo ;

Ortega, Jaime H. .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2008, 32 (11) :919-925

[3] DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS [J].

Badra, Mehdi ;

Caubet, Fabien ;

Dambrine, Marc .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2011, 21 (10) :2069-2101

[4] Stable determination of an immersed body in a stationary Stokes fluid [J].

Ballerini, Andrea .

INVERSE PROBLEMS, 2010, 26 (12)

[5] TOPOLOGICAL SENSITIVITY ANALYSIS FOR THE LOCATION OF SMALL CAVITIES IN STOKES FLOW [J].

Ben Abda, A. ;

Hassine, M. ;

Jaoua, M. ;

Masmoudi, M. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (05) :2871-2900

[6] Data completion for the Stokes system [J].

Ben Abda, Amel ;

Ben Saad, Imen ;

Hassine, Maatoug .

COMPTES RENDUS MECANIQUE, 2009, 337 (9-10) :703-708

[7] STABILITY ESTIMATES FOR A ROBIN COEFFICIENT IN THE TWO-DIMENSIONAL STOKES SYSTEM [J].

Boulakia, Muriel ;

Egloffe, Anne-Claire ;

Grandmont, Celine .

MATHEMATICAL CONTROL AND RELATED FIELDS, 2013, 3 (01) :21-49

[8] A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation [J].

Bourgeois, L .

INVERSE PROBLEMS, 2005, 21 (03) :1087-1104

[9] About identification of defects in an elastic-plastic medium from boundary measurements in the antiplane case [J].

Bourgeois, L. ;

Darde, J. .

APPLICABLE ANALYSIS, 2011, 90 (10) :1481-1497

[10] A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data [J].

Bourgeois, L. ;

Darde, J. .

INVERSE PROBLEMS, 2010, 26 (09)

← 1 2 3 4 →