Dispersion analysis of a nonconforming finite element algorithm for the Helmholtz and elastodynamics equations

FABIO IVÁN ZYSERMAN; PATRICIA M. GAUZELLINO; JUAN E. SANTOS

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

JOHN WILEY & SONS LTD

Lugar: LOndres; Año: 2003 vol. 58 p. 1381 - 1395

0029-5981

We investigate the dispersive properties of a nonconforming finite element method to solve the two dimensional Helmholtz and elastodynamics equations. The study is performed by deriving and analysing  the dispersion relations and by  evaluating the derived quantities, such as the dimensionless phase and group velocities. Also the phase difference between exact and numerical solutionsis investigated.  The studied method, which yields a linear spatial approximation, demonstrates  to be less dispersive than a conforming bilinear finite element method in the two cases shown herein. Moreover, it almost halves the number of points per wavelength necessary to reach a given accuracy when calculating the mentioned velocities in both cases here presented.