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

Authors:
J.-P. Hennart;E. H. Mund;E. del Valle
Affiliations:
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 01000 México, DF, Mexico;Service de Métrologie Nucléaire, Université Libre de Bruxelles, B-1050 Brussels, Belgium and Unité de Thermodynamique, Université Catholique de Louvain, B-1348 Louvain-La- ...;Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07738 México, DF, Mexico
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 5
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Abstract

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.