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An interior penalty method for a sixth-order elliptic equation (2011)

Gudi, T., Neilan, M.

Oxford University Press

In: IMA Journal of Numerical Analysis

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Publication Date: 2011-11-24

Description: We derive and study a 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.

Print ISSN: 0272-4979

Electronic ISSN: 1464-3642

Topics: Mathematics

Published by Oxford University Press

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