摘要:

AbstractIn the last decade or so finite element techniques have been applied with increased frequency to contaminant transport problems. Whereas most of the attention has focused on finite element approximations of spatial derivatives, standard finite difference techniques are generally used for approximation of the time derivative. Such an approach yields a scheme which is at best second order correct in time. In this study several higher order approximations of the time derivative are developed and analyzed using a finite difference approximation, and Galerkin‐type finite element approximations in conjunction with several sets of basis functions. Results obtained with the different schemes exhibit significant improvements in the numerical solution of the convective‐dispersive equat

ISSN:0029-5981    

DOI:10.1002/nme.1620120302

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620120303

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA Finite Element Method using rectangular elements is applied to solve Burgers' non‐linear equation in one space dimension. The non‐linear algebraic equations thus obtained are solved by an iteration which is equivalent to the generalized Newton method. Numerical experiments indicate that the order of accuracy is equal to 2. In two space dimensions, the method is more efficient than other methods we have tes

ISSN:0029-5981    

DOI:10.1002/nme.1620120304

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe problem of cold rolling of a composite sheet which consists of alternate layers of viscoelastic and elastic materials is studied by the finite element method. Results computed and presented graphically include the pressure distribution at the contact surface, the normal stress distribution at the middle surface and the asymmetric deformation of the surface of the sheet in contact with the roller.

ISSN:0029-5981    

DOI:10.1002/nme.1620120305

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620120306

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

ISSN:0029-5981    

DOI:10.1002/nme.1620120307

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA global variational method (GVM) not requiring the boundary conditions to be incorporated in the trial functions is described. The method is outlined for a linear differential equation and the extensions necessary to handle the non‐linear problem of the indirect design of a compressible fluid channel described. The method requires a suitable estimate of a parameter, but the results obtained for the non‐linear problem indicate that the actual value of this parameter is not critical (provided that a sufficeintly large number of trial functions is used). Comparisons are made with the results from an alternative GVM approach described in Davies and Hend

ISSN:0029-5981    

DOI:10.1002/nme.1620120308

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe problem of confined seepage of water under a hydraulic structure, through a porous medium, is considered in an appropriate abstract space. Existence and uniqueness of the solution are proved. The numerical solution is derived by means of the finite element method. An error estimate is given. A sample problems in included.

ISSN:0029-5981    

DOI:10.1002/nme.1620120309

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThis paper present a numerical method to obtain optimal quadrature formulas of Gauss type and Radau type in the sense of Sard. Using the relation between optimal quadrature formulas and nonospline functions, the optimal quadrature formula can be obtained by solving a set of no‐linear simultaneous algebraic equations induced from the interpolatory conditions of the monospline. In attempting to solve this set of non‐linear algebraic equations for numbers of knots and degrees of interpolution required in estimation problem applications insurmountable numerical errors were encountered. This paper solves the numerical problem by first reducing the number of unknowns and equations to approximately one half the original number. This is accomplished by showing and then using a symmetry property of the monospline. Second an iteration scheme which partitions the reduced order set of non‐linear algebraic equations into a linear subsystem and a non‐linear subsystem is developed to numerically solve the equations. This iteration algorithm provides the advantages of reducing the computational complexity, dynamically checking the convergence and explicitly evluating the resulting a

ISSN:0029-5981    

DOI:10.1002/nme.1620120310

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractConsiderable effort has been invested lately in the application of isoparametric finite elements for numerical solution of a wide range of applied mechanics problems. In fact, several general purpose computer programs are now available which are based upon such finite elements. In the present paper, a new application of the isoparametric finite element concept is introduced which significantly extends its usefulness for many practical structural configurations. In this application, final working or architectural drawings of the structure are made from the same (or similar) finite element model as was utilized in a structural integrity analysis. The hardware necessary to produce such drawing, a computer driven plotter or automated drafting machine, is available commercially or through most data centres, and the software concepts required are described herein.

ISSN:0029-5981    

DOI:10.1002/nme.1620120311

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY