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A dispersion relation analysis is employed here to ascertain the presence and determine the form of spurious modes as well as the dispersive nature of the finite\u2010element Galerkin mixed formulation of the two\u2010dimensional linearized shallow\u2010water equations. Nine popular finite\u2010element pairs are considered using a variety of mixed interpolation schemes. For each pair the frequency or dispersion relation is obtained and analyzed, and the dispersion properties are compared analytically and graphically with the continuous case. It is shown that certain choices of mixed interpolation schemes may lead to significant phase and group velocity errors and spurious solutions in the calculation of fast waves. The $P^{NC}_{1} - P^{}_{1}$ and RT0 pairs are identified as a promising compromise, provided the grid resolution is high relative to the Rossby radius of deformation for the RT0 element. The numerical solutions of two test problems to simulate fast waves are in good agreement with the analytical results.<\/jats:p>","DOI":"10.1137\/060650106","type":"journal-article","created":{"date-parts":[[2008,10,30]],"date-time":"2008-10-30T12:15:41Z","timestamp":1225368941000},"page":"331-360","source":"Crossref","is-referenced-by-count":66,"title":["Analysis of Numerically Induced Oscillations in 2D Finite\u2010Element Shallow\u2010Water Models Part I: Inertia\u2010Gravity Waves"],"prefix":"10.1137","volume":"29","author":[{"given":"Daniel Y.","family":"Le Roux","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Virgile","family":"Rostand","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benoit","family":"Pouliot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,2,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1999)127<1928:ANTOTC>2.0.CO;2"},{"key":"R2","unstructured":"V. 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