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We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varepsilon ^{-1}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>\u03b5<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mo>-<\/mml:mo>\n                      <mml:mn>1<\/mml:mn>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> only enters <jats:italic>polynomially<\/jats:italic>; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b3<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> sufficiently large, convergence in probability of iterates towards the deterministic Hele\u2013Shaw\/Mullins\u2013Sekerka problem in the sharp-interface limit <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varepsilon \\rightarrow 0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b5<\/mml:mi>\n                    <mml:mo>\u2192<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its \u2019strength\u2019 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b3<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins\u2013Sekerka problem. The computational results indicate that the limit for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma \\ge 1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b3<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the deterministic problem, and for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\gamma =0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b3<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> we obtain agreement with a (new) stochastic version of the Mullins\u2013Sekerka problem.<\/jats:p>","DOI":"10.1007\/s00211-021-01179-7","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T04:33:04Z","timestamp":1613709184000},"page":"505-551","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Numerical approximation of the stochastic Cahn\u2013Hilliard equation near the sharp interface limit"],"prefix":"10.1007","volume":"147","author":[{"given":"Dimitra","family":"Antonopoulou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0139ubom\u00edr","family":"Ba\u0148as","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"N\u00fcrnberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,17]]},"reference":[{"key":"1179_CR1","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/BF00375025","volume":"128","author":"ND Alikakos","year":"1994","unstructured":"Alikakos, N.D., Bates, P.W., Chen, X.: Convergence of the Cahn\u2013Hilliard equation to the Hele-Shaw model. 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