{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T21:56:51Z","timestamp":1778709411579,"version":"3.51.4"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"299","license":[{"start":{"date-parts":[[2016,8,20]],"date-time":"2016-08-20T00:00:00Z","timestamp":1471651200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.<\/p>","DOI":"10.1090\/mcom\/3016","type":"journal-article","created":{"date-parts":[[2015,8,20]],"date-time":"2015-08-20T08:26:41Z","timestamp":1440059201000},"page":"1335-1358","source":"Crossref","is-referenced-by-count":55,"title":["Weak convergence for a spatial approximation of the nonlinear stochastic heat equation"],"prefix":"10.1090","volume":"85","author":[{"given":"Adam","family":"Andersson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stig","family":"Larsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,8,20]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11118-013-9338-9","article-title":"Approximation of the invariant measure with an Euler scheme for stochastic PDEs driven by space-time white noise","volume":"40","author":"Br\u00e9hier, Charles-Edouard","year":"2014","journal-title":"Potential Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0926-2601","issn-type":"print"},{"key":"2","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387759333","edition":"3"},{"key":"3","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511666223","volume-title":"Stochastic equations in infinite dimensions","volume":"44","author":"Da Prato, Giuseppe","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0521385296"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s00245-006-0875-0","article-title":"Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schr\u00f6dinger equation","volume":"54","author":"de Bouard, Anne","year":"2006","journal-title":"Appl. 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