MÉTODO DOS ELEMENTOS FINITOS H-ADAPTATIVO: UMA NOVA TÉCNICA PARA PROJEÇÃO ISOTRÓPICA DO TAMANHO ELEMENTAR
DOI:
https://doi.org/10.26512/ripe.v2i14.21360Keywords:
Método dos elementos finitos. H-adaptatividade. Superconvergent Patch Recovery. Recuperação Quadrática do Erro.Abstract
Devido à natureza aproximadora da solução fornecida pelo Método dos Elementos Finitos, são diversas as pesquisas que têm surgido com o objetivo de quantificar, controlar ou minimizar os erros causados pela discretização da solução. Nesse contexto, uma das alternativas é o emprego de processos h-adaptativos guiados por estimadores de erros a posteriori, os quais fornecem estimativas locais dos erros. Assim, com o objetivo de satisfazer um valor de erro limite com um custo computacional reduzido, propõe-se um novo método para projeção isotrópica do tamanho elementar, denominado Recuperação Quadrática do Erro. Neste, é desenvolvido o conceito de recuperação quadrática da densidade do erro em energia, o qual, em conjunto com a solução de um problema de otimização via Método do Lagrangeano, fornece uma expressão analítica para determinação do novo tamanho do elemento. A estimativa dos erros a posteriori baseada em recuperação é dirigida mediante a recuperação do gradiente pelo clássico método Superconvergente de Recuperação de Padrões (Superconvergent Patch Recovery) (Zienkiewicz e Zhu, 1992a, 1992b). A eficiência da metodologia proposta é comprovada através da aplicação em problemas lineares escalares de engenharia, sendo a implementação numérica e a geração da malha adaptada realizada respectivamente, pelos softwares Matlab e BAMG (Bidimensional Anisotropic Mesh Generator).
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