@Article{JCM-26-6,
author = {},
title = {A Posteriori Error Estimates for Finite Element Approximations of the Cahn-Hilliard Equation and the Hele-Shaw Flow},
journal = {Journal of Computational Mathematics},
year = {2008},
volume = {26},
number = {6},
pages = {767--796},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/2008-JCM-8659},
url = {https://global-sci.com/article/84964/a-posteriori-error-estimates-for-finite-element-approximations-of-the-cahn-hilliard-equation-and-the-hele-shaw-flow}
}