Heterogeneous Multiscale Methods with Quadrilateral Finite Elements

Assyr Abdulle ()
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Assyr Abdulle: University of Basel, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 743-751 from Springer

Abstract: Abstract The Heterogeneous Multiscale Method (HMM) applied to elliptic homogenization problems has been analyzed for simplicial elements in [E, Ming, Zhang, J. Amer. Math. Soc. 18, pp. 121–156, 2005] and [Abdulle, SIAM, Multiscale Model. Simul., Vol. 4, No 2, pp.195–220, 2005.]. In this paper we discuss and analyze the use of quadrilateral (hexahedral) finite elements for the HMM applied to elliptic homogenization problem. We give H 1 and L 2 a priori estimates and discuss a strategy to recover the microscopic information. Numerical examples confirm our error estimates.

Keywords: Quadrature Formula; Multiscale Model; Scale Solution; Left Picture; Macro Element (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_72

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DOI: 10.1007/978-3-540-34288-5_72

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