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 $u_t+∆(ε∆u−ε^{-1}f(u))=0$. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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