6533b855fe1ef96bd12b0055
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On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem
Anna Hundertmark-zauškovásubject
Iterative and incremental developmentIterative methodBanach fixed-point theoremApplied MathematicsWeak solution010102 general mathematicsGeometryFixed point01 natural sciences35D30 35Q30 74F10 76D05 76D03Domain (mathematical analysis)010101 applied mathematicsMathematics - Analysis of PDEsLinearizationConvergence (routing)FOS: Mathematics0101 mathematicsAnalysisAnalysis of PDEs (math.AP)Mathematicsdescription
In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical approximation of similar problems we refer this approach as the global iterative method. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point argument, where the contractivity of the corresponding mapping is shown due to the continuous dependence of the weak solution on the given domain deformation. This estimate is obtained by remapping the problem onto a fixed domain and using appropriate divergence-free test functions involving the difference of two solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-12-01 |