摘要:

Free boundary problems of Laplace equation defined in the annulus inare numerically solved. The original problem is transformed to an optimization problem. The state equation is approximated by an equation with a penalty term which approximates one of boundary conditions on the free boundary. The flux through the free boundary is calculated by the integration of the penalty term introduced above ( Integrated Penalty Method ). This penalized optimization problem is numerically solved by finite difference method. Incomplete Cholesky decomposition combined with the conjugate gradient method is used to solve systems of linear equations. Some numerical examples are given.

ISSN:0163-0563    

DOI:10.1080/01630568108816076

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

摘要:

This paper combines Banach-Steinhaus theorems with rates of Butzer-Scherer-Westphal (1973) with two versions of a uniform boundedness principle (UBP) with rates. This leads to equivalence assertions which, as in the classical situation without rates, do not only cover tests for convergence but also tests for nonconvergence, each time with rates. The method of proof of the UBPs consists in the familiar gliding hump method, but now equipped with rates. The present approach considerably unifies and extends results concerning the sharpness of error bounds in various areas of analysis. Explicit applications are given to numerical quadrature, interpolation, multiplier theory, and to difference schemes for initial value problems.

ISSN:0163-0563    

DOI:10.1080/01630568108816077

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

摘要:

Chebychev estimation, or L∞norm estimation, has as its criterion the minimization of the largest absolute residual. This paper presents a linear programming algorithm which allows linear restrictions on the parameters, and which utilizes a reduced basis and multiple pivots.

ISSN:0163-0563    

DOI:10.1080/01630568108816078

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

摘要:

Sometimes the use of several discretization parameters in approximating the solution of the operator equation A(u) = 0 is natural or obligatory. Under reasonable assumptions we are able to show the existence of an asymptotic expansion of the global discretization error in n discretization parameters.

ISSN:0163-0563    

DOI:10.1080/01630568108816079

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

摘要:

We obtain the homogenized equations for a transmission problem in a heterogeneous material. This will require some modifications of the classical results, owing to microscopic forces.

ISSN:0163-0563    

DOI:10.1080/01630568108816080

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

摘要:

In this paper, we consider finite element schemes applied to the Dirichlet problem for the system of nonlinear elliptic equations, based on piecewise linear polynomials, and present iterative methods for solving algebraic nonlinear equations, which construct monotone sequences. Furthermore, we derive error estimates which imply uniform convergence. Our results are based on the discrete maximum principle. Finally, some typical numerical examples are given to demonstrate the usefulness of convergence results.

ISSN:0163-0563    

DOI:10.1080/01630568108816081

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568108816075

出版商:Marcel Dekker, Inc.    

年代:1981

数据来源: Taylor