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Doctoral Thesis
DOI
10.11606/T.55.2019.tde-09042019-143115
Document
Author
Full name
Vera Lucia da Rocha Lopes
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1988
Supervisor
Committee
Zago, Jose Vitorio (President)
Cassago Junior, Herminio
Moura, Carlos Antonio de
Perez, José Mario Martinez
Tygel, Martin
Title in Portuguese
SOLUCAO, POR ELEMENTOS FINITOS, DE EQUACOES DE DIFUSAO LINEARES, VIA PRINCIPIOS EXTREMOS DUAIS.
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho desenvolvemos métodos numéricos para aproximação de solução da equação do calor, baseados nos princípios extremos dúais de Noble e Sewell, onde usamos o método dos Elementos Finitos para a discretização. Exibimos um espaço de Hilbert X, uma forma bilinear's a ele associada e verificamos todas as condições do lema de Max-Milgram com as quais temos prova de existência e unicidade de solução da nossa formulação. Além disso provamos um teorema de convergência. Nós usamos funções lineares por partes no tempo e no espaço. Os problemas de minimização e maximização resultantes, são resolvidos por um método de Gradientes Conjugado matricial. Para uma precisão de 10-5, são necessárias cerca de n/20 iterações para n grande, onde n é o tamanho da discretização.
Title in English
Not available
Keywords in English
Not availavle
Abstract in English
In this work we develop numerical methods for approximate solutions of the heat equation, based on the dual extremum principies of Noble and Sewell, where we use the Finite Element Method for discretization. We exhibit a Hilbert Space X, bilinear form S associated to it and we verify ali the condi tions of Lax-Milgram's lemma with Which we get proof of existence and uniqueness of solution of our formulation.Flurtilemore we prove a convergence theorem. We use piecewise linear functions both in time- and in space. The resulting minimization and maximization problents are solved by a matricial form of the Conjugate Gradient method . For n large enough it was needed about n/20 iterations to achiev the precision of 10-5, n is the size of the discretization.
 
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Publishing Date
2019-04-09
 
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