{"status":"public","scopus_import":"1","date_published":"2021-03-09T00:00:00Z","day":"09","_id":"9352","quality_controlled":"1","department":[{"_id":"JuFi"}],"volume":59,"author":[{"full_name":"Fischer, Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dietmar","last_name":"Gallistl","full_name":"Gallistl, Dietmar"},{"last_name":"Peterseim","full_name":"Peterseim, Dietmar","first_name":"Dietmar"}],"oa_version":"Preprint","doi":"10.1137/19M1308992","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","external_id":{"arxiv":["1912.11646"],"isi":["000646030400003"]},"page":"660-674","publisher":"Society for Industrial and Applied Mathematics","issue":"2","isi":1,"title":"A priori error analysis of a numerical stochastic homogenization method","oa":1,"year":"2021","publication":"SIAM Journal on Numerical Analysis","date_updated":"2023-08-08T13:13:37Z","publication_identifier":{"issn":["0036-1429"]},"article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1912.11646"}],"citation":{"ieee":"J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of a numerical stochastic homogenization method,” <i>SIAM Journal on Numerical Analysis</i>, vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021.","apa":"Fischer, J. L., Gallistl, D., &#38; Peterseim, D. (2021). A priori error analysis of a numerical stochastic homogenization method. <i>SIAM Journal on Numerical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/19M1308992\">https://doi.org/10.1137/19M1308992</a>","chicago":"Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” <i>SIAM Journal on Numerical Analysis</i>. Society for Industrial and Applied Mathematics, 2021. <a href=\"https://doi.org/10.1137/19M1308992\">https://doi.org/10.1137/19M1308992</a>.","short":"J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis 59 (2021) 660–674.","ama":"Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical stochastic homogenization method. <i>SIAM Journal on Numerical Analysis</i>. 2021;59(2):660-674. doi:<a href=\"https://doi.org/10.1137/19M1308992\">10.1137/19M1308992</a>","ista":"Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674.","mla":"Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” <i>SIAM Journal on Numerical Analysis</i>, vol. 59, no. 2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:<a href=\"https://doi.org/10.1137/19M1308992\">10.1137/19M1308992</a>."},"abstract":[{"lang":"eng","text":"This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\\varepsilon/H)^{d/2}$, $\\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization."}],"date_created":"2021-04-25T22:01:31Z","type":"journal_article","intvolume":"        59","article_processing_charge":"No","month":"03","language":[{"iso":"eng"}],"acknowledgement":"This work was initiated while the authors enjoyed the kind hospitality of the Hausdorff Institute for Mathematics in Bonn during the trimester program Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim would like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute  for  Mathematics and Physics  (ESI), where parts of this research were developed under the frame of the thematic program Numerical Analysis of Complex PDE Models in the Sciences."}