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• W1480707903 abstract "We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite element mesh. The method modifies a given partition of unity such that optimal convergence is achieved independent of oscillation or discontinuities of the diffusion coefficient. The modification is based on an orthogonal decomposition of the solution space while preserving the partition of unity property. This precomputation involves the solution of independent problems on local subdomains of selectable size. We deduce quantitative error estimates for the method that account for the chosen amount of localization. Numerical experiments illustrate the high approximation properties even for 'cheap' parameter choices." @default.
• W1480707903 created "2016-06-24" @default.
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• W1480707903 date "2014-11-05" @default.
• W1480707903 modified "2023-10-01" @default.
• W1480707903 title "Multiscale Partition of Unity" @default.
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• W1480707903 doi "https://doi.org/10.1007/978-3-319-06898-5_10" @default.
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