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An iterative method for the reconstruction of a stationary flow
Author(s) -
Johansson Tomas,
Lesnic Daniel
Publication year - 2007
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.20205
Subject(s) - mathematics , convergence (economics) , iterative method , stokes flow , stokes problem , finite element method , partial differential equation , flow (mathematics) , initial value problem , boundary (topology) , boundary value problem , numerical analysis , mathematical analysis , mathematical optimization , geometry , physics , economics , thermodynamics , economic growth
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