{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:11:34Z","timestamp":1776863494767,"version":"3.51.2"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Appl. Math."],"published-print":{"date-parts":[[2010]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper gives an overview of adaptive discretization methods for linear\nsecond-order hyperbolic problems such as the acoustic or the elastic wave equation.\nThe emphasis is on Galerkin-type methods for spatial as well as temporal discretization,\nwhich also include variants of the Crank-Nicolson and the Newmark finite difference\nschemes. The adaptive choice of space and time meshes follows the principle of \\goaloriented\"\nadaptivity which is based on a posteriori error estimation employing the\nsolutions of auxiliary dual problems.<\/jats:p>","DOI":"10.2478\/cmam-2010-0001","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:51:41Z","timestamp":1366041101000},"page":"3-48","source":"Crossref","is-referenced-by-count":71,"title":["Adaptive Galerkin Finite Element Methods for the Wave Equation"],"prefix":"10.2478","volume":"10","author":[{"given":"W.","family":"Bangerth","sequence":"first","affiliation":[{"name":"1Department of Mathematics, Texas A M University, College Station, TX 77843-3368, USA."}]},{"given":"M.","family":"Geiger","sequence":"additional","affiliation":[{"name":"2Institute of Applied Mathematics, University of Heidelberg, 69120 Heidelberg, Germany."}]},{"given":"R.","family":"Rannacher","sequence":"additional","affiliation":[{"name":"2Institute of Applied Mathematics, University of Heidelberg, 69120 Heidelberg, Germany."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p3.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2010-0001\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:33Z","timestamp":1619101293000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/10\/1\/article-p3.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2010-0001","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2010]]}}}