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Joël Wagner
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Prof. Dr.
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Wagner
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Joël
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@ProfDrJWagner
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PublicationFinite element approximation of multi-scale elliptic problems using patches of elements(Springer, 2005-07-18)
;Glowinski, Roland ;He, Jiwen ;Lozinski, Alexei ;Rappaz, JacquesIn this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. This paper provides proofs of the results published earlier (see C. R. Acad. Sci. Paris, Ser. I 337 (2003) 679-684), gives a generalization of the latter to more than two domains and contains extensive numerical illustrations. New results including the spectral analysis of the iteration operator and a numerical method to evaluate the constant of the strengthened Cauchy-Buniakowski-Schwarz inequality are presented.Type: journal articleJournal: Numerische MathematikVolume: 101Issue: 4Scopus© Citations 32 -
PublicationA multi-domain method for solving numerically multi-scale elliptic problemsIn this paper we present a family of iterative methods to solve numerically second order elliptic problems with multi-scale data using multiple levels of grids. These methods are based upon the introduction of a Lagrange multiplier to enforce the continuity of the solution and its fluxes across interfaces. This family of methods can be interpreted as a mortar element method with complete overlapping domain decomposition for solving numerically multi-scale elliptic problems.Type: journal articleJournal: Comptes Rendus MathematiqueVolume: 338Issue: 9
Scopus© Citations 4 -
PublicationApproximation of multi-scale elliptic problems using patches of finite elementsIn this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439-456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1-21). However it is of much more flexible use in comparison to the latter.Type: journal articleJournal: Comptes Rendus MathematiqueVolume: 337Issue: 10
Scopus© Citations 21 -
PublicationFinite Element Methods with patches and Applications(Springer, 2005-01-13)
;Glowinski, Roland ;He, Jiwen ;Lozinski, Alexei ;Picasso, Marco ;Rappaz, Jacques ;Rezzonico, Vittoria ;Widl, Olof B.Keyes, David E.We present a new method [7] for numerically solving elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. We use a relaxation method that consists of calculating successive corrections to the solution in patches of finite elements. We analyse the spectral properties of the iteration operator [6]. We show how to evaluate the best relaxation parameter and what is the influence of patches size on the convergence of the method. Several numerical results in 2D and 3D are presented.Type: conference paperJournal: Lecture Notes in Computational Science and EngineeringVolume: Volume 55Scopus© Citations 1 -
PublicationApproximation of multi-scale elliptic problems using patches of finite elements(Springer, 2004-05-25)
;Rappaz, Jacques ;Glowinski, Roland ;He, JiwenLozinski, AlexeiType: conference paper