Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-2014-02826-3
Published electronically: March 24, 2014
MathSciNet review: 3246805
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N12, 65N15

Retrieve articles in all journals with MSC (2010): 65N30, 65N12, 65N15


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

DOI: https://doi.org/10.1090/S0025-5718-2014-02826-3
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.