摘要:

Numerical resolvent methods are presented for macro-hybrid mixed variational inequalities, which render Uzawa and penalty-duality type iterative algorithms. The sub differential methodology for constrained problems is extended to domain decomposition hybrid formulations. Then, systematically, finite element discretizations can be constructed, and numerical iterative algorithms are produced via resolvent characterizations and proximal-point approximations. For associated evolution problems, the algorithms are interpreted as numerical time integration schemes.

ISSN:0163-0563    

DOI:10.1080/01630569808816853

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We prove an existence theorem of Lagrange multipliers for an abstract control problem in Banach spaces. This theorem may be applied to obtain optimality conditions for control problems governed by partial differential equations in the presence of pointwise state constraints.

ISSN:0163-0563    

DOI:10.1080/01630569808816854

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We provide the numerical analysis of the combination of finite elements and Dirichlet-to-Neumann mappings (based on boundary integral operators) for a class of nonlinear exterior transmission problems whose weak formulations reduce to Lipschitz-continuous and strongly monotone operator equations. As a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane, coupled with the Laplace equation in the corresponding unbounded exterior part. A discrete Galerkin scheme is presented by using linear finite elements on a triangulation of the domain, and then applying numerical quadrature and analytical formulae to evaluate all the linear, bilinear and semilinear forms involved. We prove the unique solvability of the discrete equations, and show the strong convergence of the approximate solutions. Furthermore, assuming additional regularity on the solution of the continuous operator equation, the asymptotic rate of convergenceO(h)is also derived. Finally, numerical experiments are presented, which confirm the convergence results.

ISSN:0163-0563    

DOI:10.1080/01630569808816855

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A numerical method to solve a constrained optimal control problem governed by a generalized Ginzburg-Landau model which describes the phase transitions taking place in the superconducting thin films with variable thickness. The method is based on a finite element method to approximate the state equations and an exterior penalty function algorithm to solve the discrete optimal control problem. The convergence of the discrete optimal solutions to the continuous optimal solutions and the convergence of the exterior penalty function algorithm are proved. The objective of the work is to study efficient numerical methods for exploring the possibilities of controlling the motion of vortices in the superconducting thin films through the external magnetic field.

ISSN:0163-0563    

DOI:10.1080/01630569808816856

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We consider finite element approximations for positive solutions of the semilinear elliptic problemwith the functiona(·) changing sign, and with superlinear growth (p< 1). We expect solutions of this problem to be saddle-points of the associated energy functional, and therefore minimization techniques are not suitable for this case. However, since solutions may be characterized as constrained maxima for a different functional, we will give a discrete version of this approach and study the convergence of approximate solutions. We also present some numerical experiments.

ISSN:0163-0563    

DOI:10.1080/01630569808816857

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A class of parameter choice strategies which include an approximated version of the Arcangeli's method is considered for ill-posed operator equations when the data are not known exactly. A particular case of the method is a generalization and modification of the Marti's method, in which case the results include, and in certain cases improve the conclusions of Engl and Neubauer (1985) under weaker conditions.

ISSN:0163-0563    

DOI:10.1080/01630569808816858

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Stability for discretizations of saddle point problems is typically the result of satisfying the discrete Babuška-Brezzi condition. As a consequence a number of natural discretizations are ruled out and some effort is required to provide stable ones. Therefore ideas for circumventing the Babuška-Brezzi condition are interesting. Here an ansatz presented in a series of papers by Hughes et al. is described and investigated in the framework of multiscale discretizations. In particular discretizations for appending boundary conditions by Lagrange multipliers and the stationary Stokes problem are considered. Sufficient conditions for their stability are given and diagonal preconditioned which give uniformly bounded condition numbers are proposed.

ISSN:0163-0563    

DOI:10.1080/01630569808816859

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper is concerned with nonlinear ill-posed operator equationsF(x) =yand their approximate solution by a quasi-Newton method, namely a regularized version of Broyden's method. Under an assumption on the nonlinearity ofF(which is shown to be fulfilled for several examples of inverse problems) and with an appropriate stopping rule, local convergence and convergence rates results are proven. The theoretical results are illustrated by numerical tests.

ISSN:0163-0563    

DOI:10.1080/01630569808816860

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

An approximation of the Hammerstem integral equation with so discontinuous kernels that we are forced to look for a solution in the spaceL∞, is considered. The notion of the discrete convergence of vectors with increasing dimension to an essentially bounded function is introduced, defining a consistent system of linear piecewise integral connection operators between these spaces. Then the equation is approximated by a sequence of finite dimensional equations and the rate of the convergence of approximations is estimated.

ISSN:0163-0563    

DOI:10.1080/01630569808816861

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper, we give lower and upper bounds for the spectral norms of interpolation matrices arising from radial basis interpolation by strictly conditionally positive definite functions of orderkon the sphereSd-1.

ISSN:0163-0563    

DOI:10.1080/01630569808816862

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor