{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:40:23Z","timestamp":1776728423858,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"240","license":[{"start":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T00:00:00Z","timestamp":1042761600000},"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>\n                    This paper deals with a semi-implicit time discretization with variable step of a three-dimensional Fr\u00e9mond model for shape memory alloys. Global existence and uniqueness of a solution is discussed. Moreover, an\n                    <italic>a priori<\/italic>\n                    estimate for the discretization error is recovered. The latter depends solely on data, imposes no constraints between consecutive time steps, and shows an optimal order of convergence when referred to a simplified model.\n                  <\/p>","DOI":"10.1090\/s0025-5718-02-01409-6","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T14:12:48Z","timestamp":1032531168000},"page":"1431-1453","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of a variable time-step discretization of the three-dimensional Fr\u00e9mond model for shape memory alloys"],"prefix":"10.1090","volume":"71","author":[{"given":"Ulisse","family":"Stefanelli","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2002,1,17]]},"reference":[{"key":"1","series-title":"The IMA Volumes in Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8704-6","volume-title":"Metastability and incompletely posed problems","volume":"3","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/0387964622"},{"key":"2","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/BF02412236","article-title":"Sulle equazioni differenziali astratte lineari del primo e del secondo ordine negli spazi di Hilbert","volume":"76","author":"Baiocchi, Claudio","year":"1967","journal-title":"Ann. 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Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0033-569X","issn-type":"print"},{"issue":"9","key":"7","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1016\/0362-546X(92)90228-7","article-title":"Global existence for a three-dimensional model for the thermomechanical evolution of shape memory alloys","volume":"18","author":"Colli, Pierluigi","year":"1992","journal-title":"Nonlinear Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0362-546X","issn-type":"print"},{"issue":"5","key":"8","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1002\/mma.1670180504","article-title":"Global solution to the full one-dimensional Fr\u00e9mond model for shape memory alloys","volume":"18","author":"Colli, Pierluigi","year":"1995","journal-title":"Math. Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0170-4214","issn-type":"print"},{"key":"9","series-title":"Grundlehren der Mathematischen Wissenschaften","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66165-5","volume-title":"Inequalities in mechanics and physics","volume":"219","author":"Duvaut, G.","year":"1976","ISBN":"https:\/\/id.crossref.org\/isbn\/3540073272"},{"key":"10","unstructured":"M. Fr\u00e9mond. Mat\u00e9riaux \u00e0 m\u00e9moire de forme. C. R. Acad. Sci. Paris S\u00e9r. II M\u00e9c. Phys. Chim. Sci. Univers Sci. Terre, 304:239\u2013244, 1987."},{"issue":"18","key":"11","first-page":"1265","article-title":"Dissipation dans le changement de phase. Surfusion. Changement de phase irr\u00e9versible","volume":"301","author":"Fr\u00e9mond, Michel","year":"1985","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. II M\\'{e}c. Phys. Chim. Sci. Univers Sci. 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Shape memory alloys: mathematical models for a class of first order solid-liquid phase transitions in metals. Control Cybernet,, 19:287\u2013308, 1990."},{"key":"17","doi-asserted-by":"crossref","unstructured":"U. Stefanelli. Analisys of a variable time-step discretization for the Penrose-Fife phase relaxation problem. Nonlinear Anal., 45:213\u2013240, 2001.","DOI":"10.1016\/S0362-546X(99)00339-9"},{"issue":"5-6","key":"18","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1080\/01630569908816912","article-title":"Error control of a nonlinear evolution problem related to phase transitions","volume":"20","author":"Stefanelli, Ulisse","year":"1999","journal-title":"Numer. Funct. Anal. Optim.","ISSN":"https:\/\/id.crossref.org\/issn\/0163-0563","issn-type":"print"},{"key":"19","unstructured":"U. Stefanelli. Error control for a time-discretization of the full one-dimensional Fr\u00e9mond model for shape memory alloys. Adv. Math. Sci. 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