Showing papers on "Meshfree methods published in 1976"
TL;DR: The relationship between and relative advantages of finite difference and finite element methods are discussed in this paper, where it is shown how conservation properties are best preserved by the latter methods and, in particular, how the supression of non-linear instabilities in the advection equation is achieved by the Arakawa schemes.
27 citations
TL;DR: The degree of agreement between numerical results of the two methods and corresponding experimental test data is given and the degree of flexibility of implementation and economics (computer execution time and storage requirements) for the two techniques are compared.
Abstract: This paper presents a comparison between the finite element and difference methods applied to two dimensional nonlinear magnetic field problems. The comparison is based on the determination of the magnetic field distribution in a shell-type single phase transformer with substantial magnetic core saturation. The comparison between the two discretization schemes is based on an equal number of finite element and finite difference domains. The finite element mesh is superimposed on the finite difference grid, to assure an equitable basis of comparison. Aspects of flexibility of implementation and economics (computer execution time and storage requirements) for the two techniques are compared. In addition, the degree of agreement between numerical results of the two methods and corresponding experimental test data is given.
11 citations
01 Dec 1976
TL;DR: Finite element and finite difference methods are examined in this article, and it is shown that both methods use two types of discrete representations of continuous functions, i.e., functional approximations and finite volume difference methods.
Abstract: Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
2 citations
01 Jan 1976
TL;DR: Asymmetric linear basis functions are introduced which overcome difficulty when applied to second order elliptic equations with large coefficients of the first order terms and are shown to be oscillation free and highly accurate for the working range of mesh sizes.
Abstract: Galerkin finite element methods based on symmetric pyramid basis functions do not give good answers when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is large. In the present study asymmetric linear basis functions are introduced which overcome this difficulty. In addition, parabolic basis functions are shown to be oscillation free and highly accurate for the working range of mesh sizes.
1 citations