Applications of the combined continuous finite element and discontinuous Garlekin methods / Aplicações dos metodos de elementos finitos continuo e Garlekin descontinuo combinados

AUTOR(ES)
DATA DE PUBLICAÇÃO

2010

RESUMO

The present work is dedicated to study the continuous Finite Element Method (FEM) and the Discontinuous Galerkin Method (DGM) combined in the same simulation. In this work the DGM is dealt with as a variant of the Finite Element Method where the interpolation space is formed by discontinuous functions between elements. In this work, we propose a formulation which combines FEM and DGM in the same simulation identifying when each method has better performance. The proposed formulation is applied to second-order elliptic problems with singular solution and to convection problems. For elliptic problems, we propose the use of local enrichment function in the approximation space of discontinuous elements. Elements with enrichment functions are employed in the vicinity of singularities. In other regions, continuous elements are employed. For convection problems, we propose to use discontinuous elements in regions where the solution presents shocks and continuous elements where the solution is smooth. A strategy to automatically decide which type of element is to be adopted is proposed. The results are compared in terms of approximation errors and for convective problems also in terms of amplitude of oscillations

ASSUNTO(S)

galerkin methods finite element method metodos de numerical analysis metodo dos elementos finitos lei de conservação (fisica) conservation laws análise numérica galerkin

ACESSO AO ARTIGO

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