ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
At present there are many general methods of approximating a possibly nonlinear operator equation by a finite equation system. The most commonly applied methods are the finite element and the finite difference. Numerous papers (e.g. References 9 and 10) have dealt with a comparison of these methods.In Reference 12 the Galerkin finite difference method (GFDM) is developed. The GFDM is a special finite element method designed t o solve nonlinear and possibly coupled partial differential equations numerically. It consists of a finite difference scheme derived from a Galerkin finite element method through the use of special local basis functions and a special grid.In this paper, we are concerned with extending the GFDM to derive ‘normal’ difference schemes. e.g. five-point schemes on two-dimensional domains for a general class of operators, even in nonlinear cases.Using GFDM or the finite element method on two-dimensional regions generally leads to at least 7- or 9-point schemes as well as expensive approximations of the nonlinear terms. Often, numerical integration is necessary. These computational costs are due to the non-orthogonality of the continuous and differentiable local basis functions that are needed in this case.The basic idea of the multi-bases approaches, which are the major concern in this paper11, is to reduce the smoothnessproperties ofthelocal basis functions in favour oftheir orthogonality. Thiscan beachieved with the help of so-called transfer operators which map the non-orthogonal and differentiable basis onto an only bounded but orthogonal basis.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620210410
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