{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T10:32:49Z","timestamp":1762252369650},"reference-count":29,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of <jats:inline-formula id=\"j_cmam-2016-0022_ineq_9999_w2aab3b7e1918b1b6b1aab1c13b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>H<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:tex-math>${H^{1}}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> into the image and the kernel of some novel stable quasi-interpolation operators with local <jats:inline-formula id=\"j_cmam-2016-0022_ineq_9998_w2aab3b7e1918b1b6b1aab1c13b1b3Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>L<\/m:mi>\n                              <m:mn>2<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:tex-math>$L^{2}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-approximation properties, independent of the contrast. We identify a set of sufficient assumptions on these quasi-interpolation operators that guarantee in principle optimal convergence without pre-asymptotic effects for high-contrast coefficients. We then give an example of a suitable operator and establish the assumptions for a particular class of high-contrast coefficients. So far this is not possible without any pre-asymptotic effects, but the optimal convergence is independent of the contrast and the asymptotic range is largely improved over other discretization schemes. The new framework is sufficiently flexible to allow also for other choices of quasi-interpolation operators and the potential for fully robust numerical upscaling at high contrast.<\/jats:p>","DOI":"10.1515\/cmam-2016-0022","type":"journal-article","created":{"date-parts":[[2016,6,11]],"date-time":"2016-06-11T10:01:20Z","timestamp":1465639280000},"page":"579-603","source":"Crossref","is-referenced-by-count":24,"title":["Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast"],"prefix":"10.1515","volume":"16","author":[{"given":"Daniel","family":"Peterseim","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Numerische Simulation der Universit\u00e4t Bonn, Wegelerstr. 6, 53115 Bonn, Germany"}]},{"given":"Robert","family":"Scheichl","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom of Great Britain and Northern Ireland"}]}],"member":"374","published-online":{"date-parts":[[2016,6,11]]},"reference":[{"key":"2023033116455899359_j_cmam-2016-0022_ref_001_w2aab3b7e1918b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Babu\u0161ka I. and Lipton R.,\nThe penetration function and its application to microscale problems,\nMultiscale Model. 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