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Alexei Lozinski Zoubida Mghazli Khallih Ould Ahmed Ould Blal 《Comptes Rendus Mathematique》2013,351(7-8):271-275
This work consists of a numerical study of a multi-scale finite element method for a Stokes-type problem with highly oscillating coefficients. The objective of this method is to capture the multi-scale structure of the solution via local basis functions calculated in advance, which contain the essential information on small scales. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(1):123-127
The purpose of this Note is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite elements with meshes which do not fit on the contact zone. The mortar technique allows us to match (independent) discretizations within each solid and to express the contact conditions in a satisfying way. Then, we carry out a numerical analysis of the algorithm and, using a bootstrap argument, we give an upper bound of the convergence rate similar to that already obtained for compatible grids. 相似文献
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Résumé Nous considérons quelques extensions des résultats classiques d'estimation d'erreur pour les problèmes mixtes. Nous étudions en particulier l'effet de l'emploi d'une approximation non conforme et celui de la décomposition de la formeb(·,·) enb
1(·,·) etb
2(·,·). Nous employons cette domposition pour affiner certaines estimations dans le cas où la formea(·,·) n'est pas coercive dans la bonne norme. Nous considérons aussi des résultats de dualité dans le cas non conforme.
Analysis of a mixed finite element for the Stokes problemI. General results
Summary We consider some extensions of the classical error estimates for mixed problems. We take into account, in particular, nonconforming approximations and the splitting of the bilinear formb(·,·), intob 1(·,·) andb 2(·,·). We use this last fact to sharpen some estimates in a case where the forma(·,·) does not have coercivity in the right norm. We also consider duality results in the nonconforming case.
Ce travail a été réalisé grâce à des subventions du fonds FCAR et du CRSNG. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):707-710
In a previous study, we considered it nonconforming finite element method for a frictionless contact problem. The aim of this note is to establish the convergence of the method for a frictional contact problem between two deformable bodies. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(3):391-396
We consider some variational problems with nonlinear boundary conditions. We approximate them by some discrete problems using P1 finite elements. We know that the discrete problems converge to the continuous ones when we consider linear boundary conditions (see [1]). We are interested by the nonlinear case. Mainly, we prove convergence for this kind of problems. 相似文献
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V. Mercat 《manuscripta mathematica》1999,98(1):75-85
Let C be a smooth projective algebraic curve of genus g. The Brill–Noether problem is to determine at which conditions on n, d and k, there exists a stable vector bundle of rank n, degree d and with at least k independent global sections. Teixidor gave a rather general answer about the existence in her paper [Tei]. The result was available only for a generic curve, in a very imprecise sense, and the proof was really difficult. We show here, that the result is in fact true for all curves and a little more. Received: 5 September 1997 / Revised version: 15 June 1998 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(11):1287-1293
We construct a new family of triangular and quadrangular edge finite elements for the resolution of Maxwell equations which solves the problem of mass lumping, including the case of anisotropic media. The schemes obtained are analyzed through their numerical dispersion on regular meshes. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(10):939-942
In this Note we introduce a new three field mixed formulation to approximate the solution of a nonlinear elasticity problem based on the Raviart–Thomas type elements. The existence and uniqueness of solutions of the mixed formulation and its discretization are proved and optimal error estimates are derived. 相似文献
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Journal d'Analyse Mathématique - 相似文献
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《Journal de Mathématiques Pures et Appliquées》2002,81(7):603-640
In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam. 相似文献