An iterative method for the reconstruction of a stationary flow

Tomas Johansson; Daniel Lesnic

doi:10.1002/num.20205

An iterative method for the reconstruction of a stationary flow

Tomas Johansson, Daniel Lesnic

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

Original language	English
Pages (from-to)	998-1017
Number of pages	20
Journal	Numerical Methods for Partial Differential Equations
Volume	23
Issue number	5
Early online date	8 Jan 2007
DOIs	https://doi.org/10.1002/num.20205
Publication status	Published - Jul 2007

Keywords

boundary element method
Cauchy problem
inverse problem
regularization
Stokes flow

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abstract = "In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. {\textcopyright} 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007",

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AB - In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

KW - boundary element method

KW - Cauchy problem

KW - inverse problem

KW - regularization

KW - Stokes flow

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JF - Numerical Methods for Partial Differential Equations

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An iterative method for the reconstruction of a stationary flow

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Keywords

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