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

• 来源期刊: 计算数学(英文版)
• 关键词: Cahn-Hilliard equation Hele-Shaw flow Phase transition Conforming ele-ments Mixed finite element methods A posteriori error estimates Adaptivity
• 年，卷（期）: 2008,（6）
• 页码范围: 767-796
• 页数: 30页
• 语种: 英文

摘要

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△μ-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.