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Third order nodal finite element methods with transverse and reduced integration for elliptic problems

This paper describes a solution technique for multidimensional elliptic problems based on the use of some third order nodal finite elements and on a reduction of the basic (multidimensional) problem to a set of coupled one-dimensional problems. This solution technique, developed rather heuristically...

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Bibliographic Details
Published in:Applied numerical mathematics 2003-08, Vol.46 (2), p.209-230
Main Authors: Hennart, J.-P., Mund, E.H., del Valle, E.
Format: Article
Language:English
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Summary:This paper describes a solution technique for multidimensional elliptic problems based on the use of some third order nodal finite elements and on a reduction of the basic (multidimensional) problem to a set of coupled one-dimensional problems. This solution technique, developed rather heuristically in the framework of nuclear reactor computations in conjunction with early nodal methods, gets on a much firmer ground when applied with nodal finite elements. The first part of the paper deals with the general context of variational nodal finite element methods. The so-called “Transverse and Reduced Integration Method” is then described in the second part of the paper. Its numerical properties are illustrated by some examples.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(03)00024-2