Gloria, Antoine Reduction of the resonance error. I: Approximation of homogenized coefficients. (English) Zbl 1233.35016 Math. Models Methods Appl. Sci. 21, No. 8, 1601-1630 (2011). The author studies the issue of computing effective coefficients in the presence of resonance errors, i.e. when terms involving \(\frac{\eta}{\epsilon}\) occur. Here \(\epsilon\) refers to the length scale of the microstructures, and \(\eta\) is a characteristic macroscopic length scale. A couple of numerical examples are given. Reviewer: Adrian Muntean (Eindhoven) Cited in 1 ReviewCited in 24 Documents MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs Keywords:numerical homogenization; resonance error; effective coefficients PDFBibTeX XMLCite \textit{A. Gloria}, Math. Models Methods Appl. Sci. 21, No. 8, 1601--1630 (2011; Zbl 1233.35016) Full Text: DOI References: [1] DOI: 10.1137/S0036141003426471 · Zbl 1070.49009 · doi:10.1137/S0036141003426471 [2] DOI: 10.3934/nhm.2010.5.1 · Zbl 1262.65115 · doi:10.3934/nhm.2010.5.1 [3] DOI: 10.1016/j.anihpb.2003.07.003 · Zbl 1058.35023 · doi:10.1016/j.anihpb.2003.07.003 [4] Engquist W. E. B., Commun. Comput. Phys. 2 pp 367– [5] Ming W. E. P. B., J. Amer. Math. Soc. 18 pp 121– [6] DOI: 10.1007/978-1-4613-8156-3 · doi:10.1007/978-1-4613-8156-3 [7] DOI: 10.1137/060649112 · Zbl 1119.74038 · doi:10.1137/060649112 [8] Gloria A., Multiscale Model. Simul. 7 pp 275– [9] DOI: 10.1214/10-AOP571 · Zbl 1215.35025 · doi:10.1214/10-AOP571 [10] DOI: 10.1007/BF01166225 · Zbl 0485.35031 · doi:10.1007/BF01166225 [11] Han Q., Elliptic Partial Differential Equations (1997) · Zbl 1052.35505 [12] DOI: 10.1006/jcph.1997.5682 · Zbl 0880.73065 · doi:10.1006/jcph.1997.5682 [13] DOI: 10.1090/S0025-5718-99-01077-7 · Zbl 0922.65071 · doi:10.1090/S0025-5718-99-01077-7 [14] DOI: 10.4310/CMS.2004.v2.n2.a3 · Zbl 1085.65109 · doi:10.4310/CMS.2004.v2.n2.a3 [15] DOI: 10.1007/978-3-642-84659-5 · doi:10.1007/978-3-642-84659-5 [16] Meyers N., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 pp 189– [17] DOI: 10.1007/978-1-4612-2032-9_3 · doi:10.1007/978-1-4612-2032-9_3 [18] Vogelius M., RAIRO Modél. Math. Anal. Numér. 25 pp 483– · Zbl 0737.35126 · doi:10.1051/m2an/1991250404831 [19] DOI: 10.1016/j.jcp.2006.07.034 · Zbl 1158.74541 · doi:10.1016/j.jcp.2006.07.034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.