{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T01:53:22Z","timestamp":1787277202407,"version":"build-2736575974"},"reference-count":46,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["20020 172710"],"award-info":[{"award-number":["20020 172710"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These effective data need to be computed by running local microscale simulations followed by a local averaging of the microscopic information. Motivated by the classical homogenization theory, it is a common practice to use local elliptic cell problems for computing the missing homogenized coefficients in the macro model. Such a consideration results in a first order error [Formula: see text], where [Formula: see text] represents the wavelength of the microscale variations and [Formula: see text] is the size of the microscopic simulation boxes. This error, called \u201cresonance error,\u201d originates from the boundary conditions used in the microproblem and typically dominates all other errors in a multiscale numerical method. Optimal decay of the resonance error remains an open problem, although several interesting approaches reducing the effect of the boundary have been proposed over the last two decades. In this paper, as an attempt to resolve this problem, we propose a computationally efficient, fully elliptic approach with exponential decay of the resonance error.<\/jats:p>","DOI":"10.1137\/21m1452123","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T11:00:37Z","timestamp":1683630037000},"page":"513-541","source":"Crossref","is-referenced-by-count":3,"title":["An Elliptic Local Problem with Exponential Decay of the Resonance Error for Numerical Homogenization"],"prefix":"10.1137","volume":"21","author":[{"given":"Assyr","family":"Abdulle","sequence":"first","affiliation":[{"name":"ANMC, Institute of Mathematics, \u00c9cole Polytechnique F\u00e9d\u00e9rale DE Lausanne, Station 8, CH 1015 Lausanne, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Doghonay","family":"Arjmand","sequence":"additional","affiliation":[{"name":"ANMC, Institute of Mathematics, \u00c9cole Polytechnique F\u00e9d\u00e9rale DE Lausanne, Station 8, CH 1015 Lausanne, Switzerland."},{"name":"Department of Information Technology, Division of Scientific Computing, Uppsala University, P O Box 337, S-751 05 Uppsala, Sweden."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edoardo","family":"Paganoni","sequence":"additional","affiliation":[{"name":"ANMC, Institute of Mathematics, \u00c9cole Polytechnique F\u00e9d\u00e9rale DE Lausanne, Station 8, CH 1015 Lausanne, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/040607137"},{"key":"ref2","first-page":"135","volume":"31","author":"Abdulle A.","year":"2009","journal-title":"GAKUTO Internat. 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