{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T01:39:45Z","timestamp":1767922785032,"version":"3.49.0"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"256","license":[{"start":{"date-parts":[[2007,7,11]],"date-time":"2007-07-11T00:00:00Z","timestamp":1184112000000},"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>In this paper, we propose a two-grid finite element method for solving coupled partial differential equations, e.g., the Schr\u00f6dinger-type equation. With this method, the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid. 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