{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T07:59:19Z","timestamp":1777622359987,"version":"3.51.4"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"292","license":[{"start":{"date-parts":[[2015,10,24]],"date-time":"2015-10-24T00:00:00Z","timestamp":1445644800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>A linear wave equation on a moving surface is derived from Hamilton\u2019s principle of stationary action. The variational principle is discretized with functions that are piecewise linear in space and time. This yields a discretization of the wave equation in space by evolving surface finite elements and in time by a variational integrator, a version of the leapfrog or St\u00f6rmer\u2013Verlet method. We study stability and convergence of the full discretization in the natural time-dependent norms under the same CFL condition that is required for a fixed surface. Using a novel modified Ritz projection for evolving surfaces, we prove optimal-order error bounds. Numerical experiments illustrate the behavior of the fully discrete method.<\/p>","DOI":"10.1090\/s0025-5718-2014-02882-2","type":"journal-article","created":{"date-parts":[[2014,10,24]],"date-time":"2014-10-24T13:11:34Z","timestamp":1414156294000},"page":"513-542","source":"Crossref","is-referenced-by-count":12,"title":["Variational discretization of wave equations on evolving surfaces"],"prefix":"10.1090","volume":"84","author":[{"given":"Christian","family":"Lubich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dhia","family":"Mansour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,10,24]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/S0021-9991(02)00057-8","article-title":"Transport and diffusion of material quantities on propagating interfaces via level set methods","volume":"185","author":"Adalsteinsson, David","year":"2003","journal-title":"J. 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