Volume 8, Issue 4
Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations

Jianye Wang and Rui Ma

10.4208/aamm.2014.m834

Adv. Appl. Math. Mech., 8 (2016), pp. 517-535.

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  • Abstract

This paper is devoted to a unified a priori and a posteriori error analysis of CIP-FEM (continuous interior penalty finite element method) for second-order elliptic problems. Compared with the classic a priori error analysis in literature, our technique can easily apply for any type regularity assumption on the exact solution, especially for the case of lower H1+s weak regularity under consideration, where 0 ≤ s ≤ 1/2. Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and C´ea Lemma for conforming finite element methods can not be applied immediately when 0≤s≤1/2. To overcome this difficulty, our main idea is introducing an auxiliary C 1 finite element space in the analysis of the penalty term. The same tool is also utilized in the explicit a posteriori error analysis of CIP-FEM.

  • History

Published online: 2018-05

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