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Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model

 

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Opened Access Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model
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Author: Guillén González, Francisco Manuel
Rodríguez Bellido, María Ángeles
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2009-09
Published in: Mathematical models and methods in applied sciences, 19(9), 1713-1742
Document type: Article
Abstract: We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative linear schemes. The different unknowns are sequentially decoupled in the first scheme and in parallel form in the second one. In both cases, the whole sequences are bounded in strong norms and convergent towards the strong solution of the system, by using a generalization of the Banach’s Fixed Point Theorem. Moreover, we explicit a priori and a posteriori error estimates (respect to the weak norms), which let us to compare both schemes.
Cite: Guillén González, F.M. y Rodríguez Bellido, M.Á. (2009). Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model. Mathematical models and methods in applied sciences, 19 (9), 1713-1742.
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URI: http://hdl.handle.net/11441/40279

DOI: 10.1142/S0218202509003929

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