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Dispersion analysis of a non‐conforming finite element method for the Helmholtz and elastodynamic equations
Author(s) -
Zyserman Fabio I.,
Gauzellino Patricia M.,
Santos Juan E.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.822
Subject(s) - finite element method , helmholtz free energy , helmholtz equation , dimensionless quantity , bilinear interpolation , mathematics , mathematical analysis , dispersion (optics) , phase (matter) , mixed finite element method , finite difference , physics , mechanics , optics , boundary value problem , statistics , quantum mechanics , thermodynamics
We investigate the dispersive properties of a non‐conforming 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 solutions is investigated. The studied method, which yields a linear spatial approximation, is shown 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. Copyright © 2003 John Wiley & Sons, Ltd.