摘要:

We develop a convergence theory for identifying parameters in a general class of nonau-

ISSN:0163-0563    

DOI:10.1080/01630569808816867

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper, we study an iterative method, which includes the Kačanov method as a particular case, for solving nonlinear variational inequalities of the second kind. A convergence result is also proved under suitable assumptions. We apply our iterative method to solve an elastoplasticity problem.

ISSN:0163-0563    

DOI:10.1080/01630569808816868

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The Kačanov method is an iteration method for solving nonlinear Problems. In this paper, we apply the Kačanov method to solve the problem of quasi-Newtonian flow obeying the Carreau law. The emphasis of the paper is the derivation of aposteriorierror estimate for Kačanov iterates. A numerical example shows the efficiency of the error estimate.

ISSN:0163-0563    

DOI:10.1080/01630569808816869

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We consider a class of eigenvalue problems (EVPs) on a bounded multi-component domain Ω in the plane, consisting of a number of convex polygonal subdomains. Classical mixed Robin-Dirichlet conditions are imposed on the outer boundaries, while on the interfaces between two subdomains we impose nonlocal transition conditions of Dirichlet type. This problem extends the single-component problem, treated in [4]. The aim of the paper is twofold. First, by passing to a product Sobolev space setting, we recast the problem into the framework of abstract variational EVPs, studied e.g.in [7]. This allows us to infer the existence of exact eigenpairs, showing some useful properties. Secondly, the variational EVP may serve as the starting point for setting up variational (internal) approximation methods, such as (conforming) finite element methods (FEMs). For this purpose the proof of a density theorem is crucial. From here on, for clarity in the exposition, we restrict ourselves to a domain Ω composed of 4 rectangles. Introducing suitable (families of) finite element spacesVh1, similar convergence properties and error estimates as in [4] are obtained for the finite element approximations of the eigenpairs, both without and with numerical quadrature. The error analysis will heavily rest upon the properties of a deliberately introducedimperfectLagrange interpolant on each of the subdomains. Finally, we briefly deal with the corresponding algebraic EVP, identifying a proper basis of the product spaceVh.

ISSN:0163-0563    

DOI:10.1080/01630569808816870

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Global convergence theorems for a class of descent methods for unconstrained optimization problems in normed spaces, using multidirectional search, are proved. Exact and inexact search are considered and the results allow to define a globally convergent algorithm for an unconstrained optimal control problem which operates, at each step, on discrete approximations of the original continuous problem.

ISSN:0163-0563    

DOI:10.1080/01630569808816871

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper we define and discuss a new non-Lagrangean procedure for theweakinterpolation of a non-linear mapping on the space of continuous functions. We suppose that the mappingis defined by an empirical data setfor eachwhere the functionsxrandyrare known only by evaluation vectorsand. In this situation the Lagrangean interpolation proposed by Prenter cannot be applied. We construct a mappingsuch thatS[u]=S[x] whenu(si)=x(si) for eachi= 1,2, …,m and such thatfor eachr= 1,2,$hellip;,pand eachk= 1,2,…,n. We show that in some special circumstances theweakinterpolation becomes astronginterpolation and we also show that the interpolation operator is continuous in the strong topology at each point of the empirical data set.

ISSN:0163-0563    

DOI:10.1080/01630569808816872

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this exposition, we investigate in an extended framework the problem of simultaneous best approximation. Refinement of a formula for the subdifferential of restricted radius of ap-bounded set leads us to explore some interesting results on strong uniqueness of simultaneous best approximants. In particular, we also. deal here with simultaneous best approximation of certain sets of vector-valued functions and establish strong uniqueness of order 2 for such approximants under suitable Haar-like hypotheses.

ISSN:0163-0563    

DOI:10.1080/01630569808816873

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The principal aim of this paper is to study the stability of the solution set mapping of a system composed by an arbitrary set of linear inequalities in an infinite-dimensional space. The unknowns space is assumed to be metrizable, which allows us to measure the size of any possible perturbation. Conditions guaranteeing the closedness, the lower semicontinuity and the upper semicontmuity of this mapping, at a particular nominal system, are given in the paper. The more significant differences with respect to the finite dimensional case, previously approached in the context of the so-called semi-infinite optimization, are illustrated by means of convenient examples.

ISSN:0163-0563    

DOI:10.1080/01630569808816874

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Necessary conditions of isolated zero-points with nonzero degree (in particular, point of local minimum or maximum either saddlepoint) inRnwhich is an extension of the rule that the first derivative of a function changes a sign in every neighborhood of an isolated point of local minimum or maximum in JR1 and connected with this choice of initial approximations for the secant method are given and proved. Most of the statements are given through using the basic topological facts such as degree, the fiberings of a finite dimensional sphere, homotopy, quotient topology, etc.

ISSN:0163-0563    

DOI:10.1080/01630569808816875

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The purpose of this paper is to study the effect of numerical quadrature on the finite element approximations to the solutions of hyperbolic intego-differential equations. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived inL∞(H1)L∞(L2) norms and quasi-optimal estimate inL∞(L∞) norm using energy arguments. Further, optimalL(L2)-estimates are shown to hold with minimal smoothness assumptions on the initial functions. The analysis in the present paper not only improves upon the earlier results of Baker and Dougalis [SIAM J. Numer. Anal. 13 (1976), pp. 577-598] but also confirms the minimum smoothness assumptions of Rauch [SIAM J. Numer. Anal. 22 (1985), pp. 245-249] for purely second order hyperbolic equation with quadrature.

ISSN:0163-0563    

DOI:10.1080/01630569808816876

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor