Analysis of high order approximations by spectral interpolation applied to the Finite Element Method in elastostatics
Luís Philipe Ribeiro Almeida1; Fabio Carlos da Rocha1
1 Federal university of Sergipe
doi:10.20906/CPS/CILAMCE2017-0604
Resumo
Structural modeling requires the use of tools that guarantee the efficiency and precision in the reproduction of geometry and loading, with variable complexity. The quality of the physical solution is associated with numerical errors found in the formulation of the finite element method, which depends on both the interpolating polynomial, the bases of the nodal points and the degree of approximation. In order to overcome this difficulty, the high order approximations, consisting of both equidistant bases and orthogonal bases of Lobatto (spectral base), is used. A comparative study between these bases applied to one-dimensional and two-dimensional elastotatic problems is analyzed. To evaluate the performance of the approximations, the Lebesgue constant and the condition number are used. From these parameters, a convergence and efficiency analysis of the bases under study is performed, in the minimization or disappearance of the Runge phenomenon, as the order of the approximation is increased. Examples are evaluated and a significant improvement of results is observed when spectral interpolation is used in detriment to the equidistant base interpolation.
Palavras-chave: Finite Element Method; Spectral interpolation; Orthogonal polynomials; Lobatto base; Runge phenomenon; Lebesgue constant