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Multigrid Methods for the Biharmonic Problem with Cahn-Hilliard Boundary Conditions

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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))

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Abstract

Let \(\varOmega\;\subset\;\mathbb{R}^2\) be a bounded polygonal domain, \({V}\;=\;\left\{{v}\;\in\;H^2\left(\varOmega\right) \;:\;\partial {v}/\partial {n}\;=\;0\;\;\mathrm{on}\;\;\partial \varOmega\right\}\) and \(f\;\in\;L_2(\varOmega)\)

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Acknowledgements

This work was supported in part by the National Science Foundation under Grant No. DMS-10-16332 and by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation.

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Correspondence to Susanne C. Brenner .

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Brenner, S.C., Gu, S., Sung, Ly. (2013). Multigrid Methods for the Biharmonic Problem with Cahn-Hilliard Boundary Conditions. 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_13

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