Indicadores de erros a posteriori na aproximação de funcionais de soluções de problemas elípticos no contexto do método Galerkin descontínuo hp-adaptivo / A posteriori error indicators in the approximation of functionals of elliptic problems solutions in the context of hp-adaptive discontinuous Galerkin method

AUTOR(ES)

João Luis Gonçalves

FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

30/09/2011

RESUMO

In this work we study goal-oriented a posteriori error indicators for approximations by the discontinuous Galerkin method for the biharmonic and Poisson equations. The methodology used for the indicators is based on the dual problem associated with the functional, which is known to generate the most effective indicators. The two main error indicators based on the dual problem, obtained for second order problems, are extended to fourth order problems. We also propose a third indicator for second and fourth order problems. The characteristics of the different indicators are studied for the localization of the elements with the greatest contributions of the error, and for the characterization of the regularity of the solutions, as well as their consequences on indicators efficiency. We propose an hp-adaptive strategy specific for goal-oriented error indicators. The performed numerical experiments show that the hp-adaptive strategy works properly, and that the use of hp-adapted approximation spaces turns out to be efficient to reduce the error with a lower number of degrees of freedom. Moreover, in the examples studied, a comparison of the quality of results for the different indicators shows that it may depend on the type of singularity and of the equation treated, showing the importance of having a wider range of indicators

ASSUNTO(S)

análise de erros (matemática) galerkin métodos de equações diferenciais elipticas - soluções numericas análise de erros a posteriori error analysis (mathematics) galerkin methods differential equations elliptic posteriori error analysis

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