Estudo numérico da aplicação do método dos elementos finitos de Galerkin e dos mínimos quadrados na solução da equação da convecção-difusão-reação tridimensional / Numerical study of the application of Galerkin and least squares finite element methods in the solution of the tridimentional convection-diffusion-reaction equation

AUTOR(ES)
DATA DE PUBLICAÇÃO

2011

RESUMO

This paper the application of the Finite Element Method in variants Galerkin and Least Squares with auxiliary equations for the numerical solution of partial differential equation that models the convection-diffusion-reaction defined over a three-dimensional domain in steady state. In the spatial discretization were used hexahedrons elements with eight (linear element) and twenty-seven (quadratic element) nodes, which were adopted Lagrange interpolation functions in local coordinates. Transforming the problem of global coordinates to local coordinates, the method of Gauss-Legendre quadrature was used for numerical integration of the coefficients of the matrices of the elements. Additionally, the formulation by the two methods, a computer code was implemented to simulate the phenomenon proposed. Offering analytical solutions, several numerical error analysis were performed from L2 norms (average error in the domain) and L? (higher error in the domain), thus validating the numerical results. A real case is proposed and analyzed

ASSUNTO(S)

método dos elementos finitos galerkin métodos de mínimos quadrados métodos númericos equações diferenciais parciais finite element method galerkin methods least squares numerical methods partial differential equations

ACESSO AO ARTIGO

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