A POSTERIORI ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF THE CAHN-HILLIARD EQUATION AND THE HELE-SHAW FLOW

作者：Feng Xiaobing^*; Wu Haijun

来源：Journal of Computational Mathematics, 2008, 26(6): 767-796.

• Cahn-Hilliard equation
• Hele-Shaw flow
• Phase transition
• Conforming elements
• Mixed finite element methods
• A posteriori error estimates
• Adaptivity

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) + Delta(epsilon Delta u-epsilon(-1) f(u)) = 0. It is shown that the a posteriori error bounds depends on epsilon(-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.

• 出版日期2008-11
• 单位南京大学