{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:21:33Z","timestamp":1787329293621,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We study a finite element-based space-time discretization of the elastodynamics equation $u^{\\varepsilon}_{tt} - {\\rm div} \\sigma(\\nabla u^{\\varepsilon}) - \\varepsilon \\Delta u_t^{\\varepsilon} = 0$ for $\\varepsilon \\geq 0$, where $\\sigma = D\\phi$ and $\\phi$ is a nonconvex function. The convergence for regularization parameters $\\varepsilon &gt; 0$ of iterates to weak solutions and for the limiting problem $\\varepsilon = 0$ of iterates towards generalized solutions is shown in a general setting of data. Computational experiments are included to motivate formation and propagation of two-dimensional microstructures for decreasing values of the regularization parameter.<\/jats:p>","DOI":"10.1137\/070685166","type":"journal-article","created":{"date-parts":[[2008,6,11]],"date-time":"2008-06-11T18:02:42Z","timestamp":1213207362000},"page":"2469-2483","source":"Crossref","is-referenced-by-count":10,"title":["Convergence of a Finite Element-Based Space-Time Discretization in Elastodynamics"],"prefix":"10.1137","volume":"46","author":[{"given":"Andreas","family":"Prohl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,6,11]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01209147"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901393413"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004019"},{"key":"R4","first-page":"521","volume":"48","author":"Crouzeix M.","year":"1987","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/s0294-1449(97)80152-7"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s002050000115"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s002050100137"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141095285958"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00380893"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1997.0130"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"P. Pedregal,\n                      Parametrized Measures and Variational Principles\n                      , Birkh\u00e4user\u2013Verlag, Basel, Switzerland, 1997.","DOI":"10.1007\/978-3-0348-8886-8"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141001392141"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/116"},{"key":"R14","unstructured":"R. E. Showalter,\n                      Monotone Operators in Banach Space and Nonlinear Partial Differential Equations\n                      , AMS, Providence, RI, 1997."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01049487"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375439"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-005-0404-3"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"R. Temam,\n                      Navier-Stokes Equations\u2014Theory and Numerical Analysis\n                      , AMS Chelsea Publishing, Providence, RI, 2001, reprinted version.","DOI":"10.1090\/chel\/343"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/070685166","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:17Z","timestamp":1787325257000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/070685166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/070685166"],"URL":"https:\/\/doi.org\/10.1137\/070685166","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}