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arXiv · 2305.01353

Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation

Yaoyao Chen·Yunqing Huang·Nianyu Yi·Peimeng Yin
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Abstract

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator.

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Yaoyao Chen, Yunqing Huang, Nianyu Yi, Peimeng Yin. 2023-05-02. Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation. https://arxiv.org/abs/2305.01353

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