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

2023/05/02 by Yaoyao Chen, Yunqing Huang, Chen, Yaoyao +5 · 1 citation
Engineering · Materials Science · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2305.01353

openalex publication_date 2023/05/02 · openalex created_date 2023/05/04 · openalex updated_date 2026/07/30

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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