Showing papers by "Susanne C. Brenner published in 1996"
TL;DR: Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconformant approximation of the stationary Stokes equations.
Abstract: Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconforming P1 finite element approximation of the stationary Stokes equations. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap.
131 citations
TL;DR: In this paper, the authors discute des methodes multigrilles for les problemes dependant de parametres, and prouve que the diminution du nombre d'iterations des algorithmes est bornee independamment du parametre and du niveau de maillages, and ce dans un cadre general.
Abstract: On discute des methodes multigrilles pour les problemes dependant de parametres. On prouve que la diminution du nombre d'iterations des algorithmes est bornee independamment du parametre et du niveau de maillages, et ce dans un cadre general. On donne des exemples d'elasticite lineaire plane avec des conditions au bord de deplacement ou de traction, du probleme de poutres de Timoshenko et du probleme de plaques de Reissner-Mindlin.
90 citations
TL;DR: In this paper, a two-level additive Schwarz preconditioner is developed for the systems resulting from the discretizations of the plate bending problem by the Morley finite element, the Fraeijs de Veubeke finite element and the Zienkiewicz finite element.
Abstract: A two-level additive Schwarz preconditioner is developed for the systems resulting from the discretizations of the plate bending problem by the Morley finite element, the Fraeijs de Veubeke finite element, the Zienkiewicz finite element and the Adini finite element. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of a generous overlap.
59 citations
TL;DR: A method of preconditioning finite elements with a large number of degrees of freedom by simpler finite elements by simpler infinite elements is discussed.
Abstract: We discuss a method of preconditioning finite elements with a large number of degrees of freedom by simpler finite elements.
13 citations
TL;DR: A theory of two-level additive Schwarz preconditioners for plate elements applicable to the cases where the finite element spaces on the two levels are conforming and nested, and nonconforming and nonnested.
Abstract: We present a theory of two-level additive Schwarz preconditioners for plate elements. It is applicable to the cases where the finite element spaces on the two levels are (I) conforming and nested, (II) conforming and nonnested, and (III) nonconforming and nonnested. The condition number of the preconditioned system is independent of the mesh sizes and the number of subdomains in the case of generous overlap.
6 citations