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Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements

Author: Martin Stynes
Journal: Math. Comp. 83 (2014), 2675-2689
MSC (2010): Primary 65N30; Secondary 65N12, 65N15
Published electronically: March 24, 2014
MathSciNet review: 3246805
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Abstract: Anisotropic $ L_p$-norm error estimates are derived for the standard rectangular Raviart-Thomas elements $ RT_{[k]}(\tilde K)$ in $ \mathbb{R}^d$ for $ p\in [1, \infty ],\ k\ge 0$ and $ d \ge 2$. Here $ \tilde K$ is an affine image of an axi-parallel parallelotope $ K$. The proofs are based on a variant of the classical Poincaré inequality. The estimates derived make full use of the asymmetric nature of the vector space components of $ RT_{[k]}(\tilde K)$; a Shishkin mesh example demonstrates their superiority over previous estimates.

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Additional Information

Martin Stynes
Affiliation: Department of Mathematics, National University of Ireland, Cork, Ireland
Address at time of publication: Applied Mathematics Division, Beijing Computational Science Research Center, No. 3 He-Qing Road, Hai-Dian District, Beijing 100084, China

Received by editor(s): August 12, 2012
Received by editor(s) in revised form: April 16, 2013
Published electronically: March 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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