摘要:

There are many examples in Numerical Analysis where convergence of approximate solutions to a solution of the original problem can not be shown in the sense of a norm topology but in the sense of weak convergence ([6], [9], [10]).

ISSN:0163-0563    

DOI:10.1080/01630569008816393

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper a modification of the asymptotic expansion (AE) given by Vishik and Lyustenik for the eigenelements of a spectral problem in elliptic-elliptic singular perturbation is described. We prove that the AE is valid in Cj(ω)j=O,…,n where n is the order of AE. A finite element method (FEM) is used to compute each term and an error estimate is proved in H1(ω) and H2(ω). We give some numerical results which prove that this method is better than a direct FEM when e is small enough.

ISSN:0163-0563    

DOI:10.1080/01630569008816394

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We consider a nonlinear parabolic equation which models the secondary cooling of steel in continuous slab casting and provide quantitative stability results both for the problem of determining the solidification front from measured Cauchy data and for the inverse problem of determining a cooling strategy that leads to a prescribed solidification front. For the latter problem, also stability and convergence of Tikhonov regularization are proved.

ISSN:0163-0563    

DOI:10.1080/01630569008816395

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

LetAbe a bounded linear operator on a Hilbert spaceH, and letA+be its Moore-Penrose inverse. A proof is given thatAandA+commute if and only ifA*=PA, wherePis an invertible bounded linear operator onH. This is an extension to infinite dimensional spaces of a result known for finite dimensionalH.

ISSN:0163-0563    

DOI:10.1080/01630569008816396

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper, we want to compare two classes of multifunctions which can be used as approximating multifunctions in differentiability theory: affine and eclipsing multifunctions. We show how the notion of eclipsing multifunctions is an extension of affine multifunctions, and what kinds of difficulties arise in this extension.

ISSN:0163-0563    

DOI:10.1080/01630569008816397

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we study the convergence of the infima and of (approximate) solutions of a sequence of minimization problems. It is shown that the main assumptions needed in order to guarantee the requested convergence properties are those of the consistency and the a-regularity of the underlying functionals, conceptions which are well-known from the discretization theory of differential equations. This paper is continued by a second part in which the theoretical results are applied to a number of concrete problems.

ISSN:0163-0563    

DOI:10.1080/01630569008816398

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In the first part of this paper [8] we have provided a number of theoretical results concerning the convergence of the infima and of (approximate) solutions of a sequence of minimization problems. In this paper we apply these results to a variety of special problems. Applications are various minimum norm problems, semiinfinite programming problems, the regularization by singular perturbation, and the discretization by nonconforming finite elements.

ISSN:0163-0563    

DOI:10.1080/01630569008816399

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The best possible constant in the trace inequalityis shown to be given by a quantity in terms of the solution of an elliptic boundary value problem, where, Ω ⊂RNis a Lipschitz domain, Γ1is a measurable subset of ∂Ω, andk> 0 is fixed.

ISSN:0163-0563    

DOI:10.1080/01630569008816400

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

This paper is concerned with the approximation of solutions of nonlinear operator equations depending on a parameter For solving the augmented systems arising in predictor-corrector continuation methods, the use of iterative schemes based on updating projection techniques is discussed.

ISSN:0163-0563    

DOI:10.1080/01630569008816401

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The nonlinear multi-dimensional heat transfer problem in discontinuously heterogeneous. but piecewise homogeneous media is treated numerically by using the enthalpy lormulation, certain regularization of the contact conditions between the homogeneous subdomains (like in [1,2]), the fully implicit time discretization and linear finite elements in space with Imear interpolation and numerical integration. A convergence is proved by using a technique that does not check the time derivative of temperature. Phase transitions with a positive latent heat (i.e. Stefan problems) are covered, as well. Besides, the problem need not be of a strongly parabolic type. Some numerical experience with the nonlinear Gauss-Seidel algorithm to solve the created nonlinear algebraic systems is presented, too.

ISSN:0163-0563    

DOI:10.1080/01630569008816402

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor