Results 1  10
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10
A twolevel additive Schwarz preconditioner for nonconforming plate elements
 Numer. Math
, 1994
"... Abstract. Twolevel additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar secondorder symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergencefree no ..."
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Cited by 35 (5 self)
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Abstract. Twolevel additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar secondorder symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergencefree 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. 1.
Convergence of nonconforming multigrid methods without full elliptic regularity
 Math. Comp
, 1995
"... Abstract. We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound (< 1) for the contraction number of the Wcycle algorithm which is independent of ..."
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Cited by 13 (0 self)
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Abstract. We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound (< 1) for the contraction number of the Wcycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable Vcycle algorithm is an optimal preconditioner. 1.
Analysis of a class of nonconforming finite elements for crystalline microstructures
 Math. Comp
, 1996
"... Abstract. An analysis is given for a class of nonconforming Lagrangetype finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed i ..."
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Cited by 8 (3 self)
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Abstract. An analysis is given for a class of nonconforming Lagrangetype finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed in 1992 by Rannacher and Turek for the Stokes equation. Our analysis highlights the features of these elements which make them effective for the computation of microstructure. New results for superconvergence and numerical quadrature are also given. 1.
A robust nonconforming H 2 –element
 Math. Comp
, 2001
"... Abstract. Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample ..."
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Cited by 6 (3 self)
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Abstract. Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming H2element which is H1conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter. 1.
Preconditioned Iterative Methods for Scattered Data Interpolation
, 2001
"... ... this paper is to study preconditioned iterative methods for the corresponding discrete systems. We introduce block diagonal preconditioners, where a multigrid operator is used for the differential equation part of the system, while we propose an operator constructed from thin plate radial basis ..."
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Cited by 1 (1 self)
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... this paper is to study preconditioned iterative methods for the corresponding discrete systems. We introduce block diagonal preconditioners, where a multigrid operator is used for the differential equation part of the system, while we propose an operator constructed from thin plate radial basis functions for the equations corresponding to the interpolation conditions. The effect of the preconditioners are documented by numerical experiments.
A Robust Nonconforming H²Element
 element, Math. Comp
"... Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counter example is given ..."
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Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counter example is given to show that the Morley method diverges for the reduced second order equation. As an alternative to the Morley element we propose to use a nonconforming H 2 element which is H 1 conforming. We show that the new finite element method converges in the energy norm uniformly in the perturbation parameter. 1.
A Mortar Finite Element Method for Plate Problems
, 2001
"... This paper is concerned with the mortar method where locally in the subdomains the nonconforming Adini and Morley plate finite elements are used. We restrict ourselves to the geometrically conforming version of the mortar method, i.e. the local substructures form a coarse triangulation. We first int ..."
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This paper is concerned with the mortar method where locally in the subdomains the nonconforming Adini and Morley plate finite elements are used. We restrict ourselves to the geometrically conforming version of the mortar method, i.e. the local substructures form a coarse triangulation. We first introduce independent local discretizations for the two discussed elements in each subdomain. The 2D triangulations of two neighboring subregions do not necessarily match on their common interface, cf. Figure 1. The mortar technique for nonconforming plate elements which is discussed here requires the continuity of the solution at the vertices of subdomains and that the solution on two neighboring subdomains satisfies two mortar conditions of the L
Finite Element Center
 Comput. Methods Appl. Mech. Engrg
, 2001
"... In this note we present a residualbased a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and genera ..."
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In this note we present a residualbased a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
EQUIVALENCE OF FINITE ELEMENT METHODS FOR PROBLEMS IN ELASTICITY*
"... Abstract. Modifications of the Morley method for the approximation of the biharmonic equation are obtained from various finite element methods applied to the equations of linear isotropic elasticity and the stationary Stokes equations, by elimination procedures analogous to those used in the continu ..."
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Abstract. Modifications of the Morley method for the approximation of the biharmonic equation are obtained from various finite element methods applied to the equations of linear isotropic elasticity and the stationary Stokes equations, by elimination procedures analogous to those used in the continuous case. Problems with Korn’s first inequality for nonconforming P1 elements and its implications for the approximation of the elasticity equations are also discussed. Key words, biharmonic, stokes, elasticity, finite element AMS(MOS) subject classifications. 65N30, 73K25 1. Introduction. It
19. A Mortar Finite Element Method for Plate Problems
"... In the paper we discuss two versions of mortar finite element methods applied to clamped plate problems. The problems are approximated by the nonconforming Morley and Adini element methods in each subregion into which the original region of the discussed problems have been partitioned. On the interf ..."
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In the paper we discuss two versions of mortar finite element methods applied to clamped plate problems. The problems are approximated by the nonconforming Morley and Adini element methods in each subregion into which the original region of the discussed problems have been partitioned. On the interfaces between subdomains and