Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements
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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.References
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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
- Email: m.stynes@ucc.ie
- Received by editor(s): August 12, 2012
- Received by editor(s) in revised form: April 16, 2013
- Published electronically: March 24, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 2675-2689
- MSC (2010): Primary 65N30; Secondary 65N12, 65N15
- DOI: https://doi.org/10.1090/S0025-5718-2014-02826-3
- MathSciNet review: 3246805