摘要:

An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function likewherehis the discretization parameter andis an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization process. The estimates obtained in the abstract case are applied to a distributed control problem and to a boundary control problem.

ISSN:0163-0563    

DOI:10.1080/01630569808816838

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Let (xn) and (◯n) be two vector sequences converging to a common limit. First, we shall define nonlinear hybrid procedures which consist of constructing a new vector sequence (yn) with better convergence properties than (xn) and (◯n). Then, this procedure is used for accelerating the convergence of a given sequence and applied to the construction of fixed point methods. New methods are derived. Finally, the connection between fixed point iterations and methods for the numerical integration of differential equations is also exploited. Numerical results are given.

ISSN:0163-0563    

DOI:10.1080/01630569808816839

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We consider two optimal control problems for first order martensitic phase transitions in a deformation-driven experiment on shape memory alloys including state constraints for the total stress and the temperature. We control by the elongation of a thin rod and by the outside temperature. The control problems are stated, and the necessary conditions of optimality are derived.

ISSN:0163-0563    

DOI:10.1080/01630569808816840

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We introduce a new family of multipoint methods of R-order two to approximate a solution of nonlinear operators equation in Banach spaces. An existence-uniqueness theorem and error estimates are provided for this family of iterations using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. For a special choice of the parameter involved, we obtain the Midpoint method, whose order of convergence is three.

ISSN:0163-0563    

DOI:10.1080/01630569808816841

出版商:Marcel Dekker, Inc    

年代:1998

数据来源: Taylor

摘要:

We consider the following singularly perturbed reaction-diffusion equationwith a small parameter € > 0 and double obstacle potential ψ. The zero level set ofapproximates the evolution of a surfaceof codimension 1, which moves in its inner normal direction with velocityThis approach is insensitive to the choice of the potential ψ and thus differs from the usual Allen-Cahn approximation. We prove optimal interface error estimates of order O(€2), for smooth flows. To this aim we construct proper barriers dictated by formal asymptotics, we introduce a modified distance function, and we exploit the validity of a comparison lemma. Finally we present some numerical results.

ISSN:0163-0563    

DOI:10.1080/01630569808816842

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper considers three types of redundant constraints in systems of an arbitrary number of inequalities posed on real locally convex spaces. The properties of each class of redundant constraints are analized and different classification criteria are given, some of them extending well-known redundancy tests for ordinary linear systems. The paper also provides results for more paticular families of linear systems, for instance, systems with either finitely many unknowns (constraints systems in semi-infinite optimization) or finitely many inequalities (constraints systems in certain moment problems)

ISSN:0163-0563    

DOI:10.1080/01630569808816843

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Let a Banach space E be ordered by a normal solid cone. In case A is a continuous quasimonotone increasing operator we prove that, for a single strictly positive element p, impliesfor a suitable chosen norm and all x in E. We give some application to ordinary and partial differential equations.

ISSN:0163-0563    

DOI:10.1080/01630569808816844

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper we show the strong convergence of an Ishikawa type iteration for a pair of nonlinear contractive type mappings S,T in a complete metric space. If S = T, this reduces to the result due to Rhoades [5] in a Banach space setting. Further, we give an easy application on a complete metric space which is convex in the sense of Takahashi [6], which generalizes the results due to Mishra and Kalinde [4] and Ding [2].

ISSN:0163-0563    

DOI:10.1080/01630569808816845

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper we introduce a finite element approximation for a parabolic hemivariational initial boundary value problem. We prove that the approximate problem is solvable and its solutions converge on subsequences to the solutions of the continuous problem

ISSN:0163-0563    

DOI:10.1080/01630569808816846

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Existence and approximation to the operator inclusionis discussed in this paper. The operator F may be noncompact. We will discuss seperately the cases when (i). F has closed graph and (ii). F is weakly sequentially continuous.

ISSN:0163-0563    

DOI:10.1080/01630569808816847

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor