A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, p. 675-696

This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way, the good stability properties of continuous-pressure mixed finite element approximations of the Stokes system are preserved. Estimates ensuring that each iteration can be performed in a stable way as well as a proof of the convergence of the iterative process provide a theoretical background for the application of the related solving procedure. Finally some numerical experiments are given to demonstrate the effectiveness of the approach, and particularly to compare its efficiency with an adaptation to this framework of a standard FETI-DP method.

DOI : https://doi.org/10.1051/m2an/2010070
Classification:  76D07,  65N55,  65N30
Keywords: Stokes equations, incompressible fluids, domain decomposition methods, non-overlapping domain decomposition methods, FETI-DP methods, cross points
@article{M2AN_2011__45_4_675_0,
     author = {Benhassine, Hani and Bendali, Abderrahmane},
     title = {A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {4},
     year = {2011},
     pages = {675-696},
     doi = {10.1051/m2an/2010070},
     zbl = {1267.76022},
     mrnumber = {2804655},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_4_675_0}
}
Benhassine, Hani; Bendali, Abderrahmane. A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, pp. 675-696. doi : 10.1051/m2an/2010070. http://www.numdam.org/item/M2AN_2011__45_4_675_0/

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