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arXiv · 1702.02603

Superconvergence analysis of partially penalized immersed finite element method

Hailong Guo·Xu Yang·Zhimin Zhang
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Abstract

The contribution of this paper contains two parts: first, we prove a supercloseness result for the partially penalized immersed finite element (PPIFE) method in [T. Lin, Y. Lin, and X. Zhang, SIAM J. Numer. Anal., 53 (2015), 1121--1144]; then based on the supercloseness result, we show that the gradient recovery method proposed in our previous work [H. Guo and X. Yang, arXiv: 1608.00063] can be applied to the PPIFE method and the recovered gradient converges to the exact gradient with a superconvergent rate $\mathcal{O}(h^{3/2})$. Hence, the gradient recovery method provides an asymptotically exact a posteriori error estimator for the PPIFE method. Several numerical examples are presented to verify our theoretical result.

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Hailong Guo, Xu Yang, Zhimin Zhang. 2017-02-08. Superconvergence analysis of partially penalized immersed finite element method. https://arxiv.org/abs/1702.02603

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