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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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|
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