A Posteriori Error Estimates for Finite Element Approximations of the Cahn-Hilliard Equation and the Hele-Shaw Flow
Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 6 : pp. 767–796
Abstract
This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut+∆(ε∆u−ε−1f(u))=0. It is shown that the a posteriori error bounds depends on ε−1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct an adaptive algorithm for computing the solution of the Cahn-Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-8659
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 6 : pp. 767–796
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Cahn-Hilliard equation Hele-Shaw flow Phase transition Conforming elements Mixed finite element methods A posteriori error estimates Adaptivity