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Localized orthogona...
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Abdulle, Assyr
(författare)
Localized orthogonal decomposition method for the wave equation with a continuum of scales
- Artikel/kapitelEngelska2017
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American Mathematical Society (AMS),2017
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LIBRIS-ID:oai:DiVA.org:kth-201763
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-201763URI
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https://doi.org/10.1090/mcom/3114DOI
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Språk:engelska
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Sammanfattning på:engelska
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QC 20170221
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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 L∞(L2)-, W1,∞(L2)-and L∞(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.
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Henning, PatrickKTH,Numerisk analys, NA(Swepub:kth)u1t7i9xk
(författare)
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KTHNumerisk analys, NA
(creator_code:org_t)
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Ingår i:Mathematics of Computation: American Mathematical Society (AMS)86:304, s. 549-5870025-57181088-6842
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