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Robust Coarsening in Multiscale PDEs

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Abstract

Consider a variationally–posed second–order elliptic boundary value problem \(a(u, \nu) \equiv \int_{\varOmega} {\mathcal{A}} (\boldsymbol {\rm{X}}) \nabla{u}.\nabla{\nu} = \int_{\varOmega} f (\boldsymbol{\rm{X}})\nu(\boldsymbol {\rm{X}}),\quad\quad {\rm{for\,\,all}}\,\,\nu \in H^{1}_{0} {\varOmega},\) with solution \(u \in H^{1}_{0} {\varOmega}\) and domain \({\varOmega} \subset {\mathbb{R}}^{d}, d = 2,3,\) where the coefficient tensor \( {\mathcal{A}} (\boldsymbol {\rm{X}})\) is highly heterogeneous (possibly in a spatially complicated way).

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Author information

Authors and Affiliations

  1. Dept. Mathematical Sciences, University of Bath, Bath, UK

    Robert Scheichl

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  1. Robert Scheichl
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Correspondence to Robert Scheichl .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Scheichl, R. (2013). Robust Coarsening in Multiscale PDEs. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_5

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