An iterative method for the reconstruction of a stationary flow

Numerical Methods for Partial Differential Equations

Volumn 23, Issue 5, 2007, Pages 998-1017

  Johansson, Tomas ^a   Lesnic, Daniel ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Boundary element method; Cauchy problem; Inverse problem; Regularization; Stokes flow

Indexed keywords

EID: 34548528952     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20205     Document Type: Article

References (22)

1. 1 G. P. Galdi, An introduction to the mathematical theory of the Navier‐Stokes equations, Vol. I, Springer‐Verlag, New York, 1994.
2. 2 J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, 1923.
3. 3 A. Zeb, L. Elliott, D. B. Ingham, and D. Lesnic, Boundary element two‐dimensional solution of an inverse Stokes problem, Eng Anal Boundary Elements 24 ( 2000), 75–88.
4. 4 A. Curteanu, Laplacian decomposition of some direct and inverse problems in fluid flows, PhD Thesis, University of Leeds, Leeds, UK, 2005.
5. 5 D. Lesnic, L. Elliott, and D. B. Ingham, An alternating boundary element method for solving Cauchy problems for the biharmonic equation, Inverse Problems Eng 5 ( 1997), 145–168.
6. 6 V. A. Kozlov, V. G. Maz'ya, and A. V. Fomin, The inverse problem of coupled thermoelasticity, Inverse Problems 10 ( 1994), 153–160.
7. 7 R. Lattès and J.‐L. Lions, The method of quasi‐reversibility, applications to partial differential equations, American Elsevier Publishing, New York, 1969.
8. 8 V. A. Kozlov and V. G. Maz'ya, On iterative procedures for solving ill‐posed boundary value problems that preserve differential equations, Algebra i Analiz 1 ( 1989), 144–170 (English transl.: Leningrad Math J 1 (1990), 1207–1228).
9. 9 V. A. Kozlov, V. G. Maz'ya, and A. V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations, Zh Vychisl Mat i Mat Fiz 31 ( 1991), 64–74 (English transl.: USSR Comput Maths Math Phys 31 (1991), 45–52).
10. 10 G. Bastay, T. Johansson, V. A. Kozlov, and D. Lesnic, An alternating method for the stationary Stokes system, ZAMM 86 ( 2006), 268–280.
11. 11 G. Bastay, V. A. Kozlov, and B. O. Turesson, Iterative methods for an inverse heat conduction problem, J Inv Ill‐posed Probl 9 ( 2001), 375–388.
12. 12 L. Marin and D. Lesnic, Boundary element Landweber method for the Cauchy problem in linear elasticity, IMA J Appl Math 70 ( 2005), 323–340.
13. 13 T. Johansson, An iterative procedure for solving a Cauchy problem for second order elliptic equations, Math Nachr 272 ( 2004), 46–54.
14. 14 T. Johansson, Reconstruction of Flow and Temperature from Boundary Data, Linköping Studies in Science and Technology, Dissertations No. 832, Linköping University, Campus Norrköping, Norrköping, 2003.
15. 15 A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations, Comm Pure Appl Math 8 ( 1955), 503–538.
16. 16 R. Regbaoui, Strong unique continuation for Stokes equation, Comm Partial Differential Eq 24 ( 1999), 1891–1902.
17. 17 H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers Group, Dordrecht, 1996.
18. 18 V. A. Morozov, On the solution of functional equations by the method of regularization, Dokl Akad Nauk SSSR 167 ( 1966), 510–512 (English transl.: Soviet Mathematics Doklady 7 (1966), 414–417).
19. 19 O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach, New York, 1963.
20. 20 A. Zeb, L. Elliott, D. B. Ingham, and D. Lesnic, The boundary element method for the solution of Stokes equations in two‐dimensional domains, Eng Anal Boundary Elements 22 ( 1998), 317–326.
21. 21 H. Power and J. E. Gomez, The completed second kind integral formulation for Stokes flow with mixed boundary conditions, Comm Numer Meth Eng 17 ( 2001), 215–227.
22. 22 W. Varnhorn, Efficient quadrature for a boundary element method to compute three‐dimensional Stokes flow, Int J Numer Meth Fluids 9 ( 1989), 185–191.