{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:37:32Z","timestamp":1648892252004},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, the method of lines approximation for a rather general\nelliptic equation containing a diffusion coefficient is considered. Our main results are\nthe regularization of the ill-posed Cauchy problem and the proof of error estimates\nleading to convergence results for the method of lines. These results are based on the\nconditional stability of the continuous Cauchy problem and the approximation by appropriately\nchosen finite-dimensional spaces, onto which the possibly perturbed Cauchy\ndata are projected. At the end of this paper, we present and discuss results of some of\nour numerical computations. There are multiple applications in material sciences, thermodynamics,\nmedicine etc.; related problems are shape optimization problems which\nare important, e.g. for nondestructive testing, crack location, thermal tomography,\nand other applications.<\/jats:p>","DOI":"10.2478\/cmam-2009-0008","type":"journal-article","created":{"date-parts":[[2013,4,15]],"date-time":"2013-04-15T15:49:53Z","timestamp":1366040993000},"page":"123-153","source":"Crossref","is-referenced-by-count":0,"title":["Method of Lines Approximations to Cauchy Problems for Elliptic Equations in Two Dimensions"],"prefix":"10.2478","volume":"9","author":[{"given":"M.","family":"Charton","sequence":"first","affiliation":[{"name":"1University of Siegen, Department of Mathematics, Walter-Flex-Str. 3, 57068 Siegen, Germany."}]},{"given":"H.J.","family":"Reinhardt","sequence":"additional","affiliation":[{"name":"1University of Siegen, Department of Mathematics, Walter-Flex-Str. 3, 57068 Siegen, Germany."}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/2\/article-p123.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/cmam-2009-0008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T14:21:23Z","timestamp":1619101283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/9\/2\/article-p123.xml"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/cmam-2009-0008","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}