An interior penalty method for a sixth-order elliptic equation

作者：Gudi Thirupathi; Neilan Michael^*

来源：IMA Journal of Numerical Analysis, 2011, 31(4): 1734-1753.

DOI：10.1093/imanum/drq031

• interior penalty method
• sixth order
• convergence analysis

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.

• 出版日期2011-10