Formulações Semi-Discretas para a Equação 1D de Burgers
DOI:
https://doi.org/10.5540/tema.2013.014.03.0319Abstract
Neste trabalho fizemos comparações entre formulações semi-discretas para a obtenção de soluções numéricas para a equação 1D de Burgers. As formulações consistem em discretizar o domínio temporal via métodos implícitos multiestágios de segunda e quarta ordem: aproximantes de Padé R11 e R22; e o domínio espacial via métodos de elementos finitos: mínimos quadrados (MEFMQ), Galerkin (MEFG) e Streamline-Upwind Petrov-Galerkin (SUPG). Conhecendo as soluções analíticas da equação 1D de Burgues, para diferentes condições iniciais e de fronteira, foram realizadas análises dos erros numéricos a partir das normas L2 e Linf. Verificamos que o método com o aproximante de Padé R22 adicionado as formulações MEFMQ, MEFG e SUPG, aumentou a região de convergência das soluções numéricas e apresentou maior precisão quando comparado as soluções obtidas por meio do aproximante de Padé R11. Constamos que o método R22 amenizou as oscilações das soluções numéricas associadas as formulações MEFG e SUPG.
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