Fine stability constants and error bounds for asymmetric approximate saddle point problems

The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle-point formulation is well established since many decades. However, this topic was mostly studied for variational formulations defined upon the same finite-element product spaces of both shape- and test-pairs of primal variable-multiplier. Whenever these two product spaces are different the saddle point problem is asymmetric. It turns out that the conditions to be satisfied by the finite elements product spaces stipulated in the few works on this case may be of limited use in practice. The purpose of this paper is to provide an in-depth analysis of the well-posedness and the uniform stability of asymmetric approximate saddle point problems, based on the theory of continuous linear operators on Hilbert spaces. Our approach leads to necessary and sufficient conditions for such properties to hold, expressed in a readily exploitable form with fine constants. In particular standard interpolation theory suffices to estimate the error of a conforming method.Comment: 6 pages Keywords: Asymmetric; Mixed finite elements; Saddle point; Uniform stability; Weak coercivit

On the strong maximum principle for some piecewise linear finite element approximative problems of non-positive type

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Sur l'application de quelques méthodes d'éléments finis à la résolution d'un problème d'élasticite incompressible non linéaire

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Indexação automática baseada em métodos lingüísticos e estatísticos e sua aplicabilidade à língua portuguesa

Considera-se neste artigo a indexação automática usando o processamento de documentos em linguagem natural, que é obtido com o auxílio de métodos linguísticos combinados com métodos estatísticos permitindo uma indexação ponderada. A título ilustrativo descreve-set em linhas gerais, um sistema de indexação desse género denominado SPIRIT, o qual foi desenvolvido para o idioma francês por uma equipe de pesquisadores do CNRS. Enfim, são tratados aspectos essenciais de sua adaptação à língua portuguesa. Descritores Ambiguidade. Análise sintética. Entropia. Estatística. Filtros. Indexação automática. Indexação ponderada. Linguística. Matrizes de precedência. Método de aprendizado. Proximidade. Relações léxicosemânticas. Abstract This paper deals with automatic indexing based on linguistic and statistical methods, which aims to allow the processing of documents in natural language. The main lines of a system called SPIRIT, that uses such methods, and that was developed for the French Languages by a group of researchers of the CNRS, including the first author,is described. Some basic aspects of the applicability of those methods to the Portuguese Language are considered