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Localized orthogonal decomposition method for the wave equation with a continuum of scales
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-6432-5504
2017 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 86, no 304, p. 549-587Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with an L2-projection. We derive explicit convergence rates of the method in the Lāˆž(L2)-, W1,āˆž(L2)-and Lāˆž(H1)-norms without any assumptions on higher order space regularity or scale-separation. The order of the convergence rates depends on further graded assumptions on the initial data. We also prove the convergence of the method in the framework of G-convergence without any structural assumptions on the initial data, i.e. without assuming that it is well-prepared. This rigorously justifies the method. Finally, the performance of the method is demonstrated in numerical experiments.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017. Vol. 86, no 304, p. 549-587
Keywords [en]
Finite element, LOD, Multiscale method, Numerical homogenization, Wave equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-201763DOI: 10.1090/mcom/3114ISI: 000391546700003Scopus ID: 2-s2.0-85008488032OAI: oai:DiVA.org:kth-201763DiVA, id: diva2:1075789
Note

QC 20170221

Available from: 2017-02-21 Created: 2017-02-21 Last updated: 2017-06-15Bibliographically approved

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  • en-US
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  • nn-NB
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  • Other locale
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