The sub-Cauchy-Stokes problem: Solvability issues and Lagrange multiplier methods with artificial boundary conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:338

Article

Ahmed, Elyes^1,2  Ben Abda, Amel³ 

[1] Inria Paris, 2 Rue Simone Iff, F-75589 Paris 12, France

[2] Univ Paris 13, UMR 7539, LAGA, F-93430 Villetaneuse, France

[3] Univ Tunis El Manar, LR99ES20, LAMSIN ENIT, BP 37, Tunis 1002, Tunisia

关键词: Inverse problem;    Sub-Cauchy-Stokes system;    Uniqueness;    Ventcell boundary conditions;    Alternating method;    Convergence factor;   

DOI  :  10.1016/j.cam.2018.01.034

来源: Elsevier

【 摘 要 】

In contrast to the conventional Cauchy-Stokes problems, in which the velocity and the stress force data are given on the accessible boundary, in the present paper, we reduce the accessible boundary data information and we consider a problem which deals only with shear stress data. We refer to this problem as a sub-Cauchy-Stokes problem. This problem is ill-posed because of severe instability and even uniqueness is unknown. We first address the uniqueness issues associated with this problem. Resorting to the domain decomposition techniques together with the duplication process of Vogelius (Kohn and Vogelius, 1985), we propose new Lagrange multiplier methods to solve the sub-Cauchy-Stokes problem. These methods consist in recasting the problem in terms of interfacial equations, by equalizing two solutions of the sub-Cauchy-Stokes problem using matching conditions defined on the inaccessible boundary. The matching is based on second order conditions and the types of the interfacial equations depend on the equations used to match the values of the unknowns on the inaccessible boundary. The interfacial problems are then solved by iterative procedures in which coefficients can be optimized to improve convergence rates. A complete analysis of the methods is presented, and intensive numerical results illustrate the effectiveness and the performance of the proposed approaches. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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