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An interior penalty method for a sixth-order elliptic equation

Gudi, Thirupathi and Neilan, Michael (2011) An interior penalty method for a sixth-order elliptic equation. In: IMA Journal of Numerical Analysis, 31 (4). pp. 1734-1753.

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Official URL: http://imajna.oxfordjournals.org/content/31/4/1734

Abstract

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Oxford University Press.
Keywords: interior penalty method;sixth order;convergence analysis
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 17 Nov 2011 09:16
Last Modified: 17 Nov 2011 09:16
URI: http://eprints.iisc.ernet.in/id/eprint/42078

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