Dispersion analysis of a nonconforming finite element method for the three dimensional scalar and elastic wave equations

FABIO IVÁN ZYSERMAN; PATRICIA MERCEDES GAUZELLINO

FINITE ELEMENTS IN ANALYSIS AND DESIGN

Elsevier

Año: 2005 vol. 41 p. 1309 - 1326

0168-874X

We investigate the dispersive properties of a nonconforming finite elementmethod (NC-method) to solve the three-dimensional scalar and elastic wave equations. The study is performed by constructing and analyzing the dispersion relations, andby evaluating derived quantities such as dimensionless phase and group velocities. Thebehaviour of the present algorithm is compared with that of a conformingfinite element method (C-method) with the same order of spatial approximation. It isobserved that the NC-method introduces less numerical anisotropy and dispersion than the C-method, allowing to work with fewer than ten points per wavelength with reasonably small relative errors. On the other hand, the computational cost of the NC-method is higher than that of the C-method. However, the present NC-method is  suitable for domain decomposed parallel algorithms;   therefore the fact that the NC-method needs more computing time may be partially  compensated by its lower transmition load.