{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:49Z","timestamp":1787337229322,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p>Shallow-water models typically employ gridpoint, finite, and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity, and\/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The triangular finite-element pair $P^{NC}_{1}-P^{}_{1}$ is shown to \"properly\" model the dispersion of the inertia-gravity waves, and this is achieved at a reasonable computational cost compared to traditional finite-difference schemes. Two tests are proposed. The first test examines the propagation and dispersion of fast surface gravity waves in a circular basin and their reflection at the lateral boundary. In the second test, results of the Stommel problem are presented using the proposed finite-element pair and are compared with those obtained with the C- and CD-finite-difference grids. They illustrate the promise of the proposed approach.<\/jats:p>","DOI":"10.1137\/030602435","type":"journal-article","created":{"date-parts":[[2005,10,5]],"date-time":"2005-10-05T21:00:22Z","timestamp":1128546022000},"page":"394-414","source":"Crossref","is-referenced-by-count":38,"title":["Dispersion Relation Analysis of the $P^NC_1 - P^_1$ Finite-Element Pair in Shallow-Water Models"],"prefix":"10.1137","volume":"27","author":[{"given":"Daniel Y.","family":"Le Roux","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1999)127<1928:ANTOTC>2.0.CO;2"},{"key":"R2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/B978-0-12-460817-7.50009-4","volume":"17","author":"Arakawa A.","year":"1977","journal-title":"Methods Comput. 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