Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods

作     者：Yanping Chen Peng Luan Zuliang Lu 

作者机构：School of Mathematical ScienceSouth China Normal UniversityGuangzhou 510631GuangdongChina Mathematics Teaching and Research GroupSanshui Experimental High School of Zhongshan UniversityFoshan 528145GuangdongChina Hunan Key Lab for Computation and Simulation in Science and EngineeringDepartment of MathematicsXiangtan UniversityXiangtan 411105HunanChina 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2009年第1卷第6期

页      面：830-844页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008) National Science Foundation of China 10971074 the National Basic Research Program under the Grant 2005CB321703 Hunan Provincial Innovation Foundation For Postgraduate CX2009B119 

主　　题：Nonlinear parabolic equations two-grid scheme expanded mixed finite element methods Gronwall’s Lemma 

摘      要：In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element *** use two Newton iterations on the fine grid in our ***,we solve an original nonlinear problem on the coarse nonlinear grid,then we use Newton iterations on the fine grid *** two-grid idea is from Xu s work[SIAM ***.,33(1996),pp.1759–1777]on standard finite *** also obtain the error estimates for the algorithms of the two-grid *** is shown that the algorithm achieve asymptotically optimal approximation rate with the two-grid methods as long as the mesh sizes satisfy h=O(H^((4k+1)/(k+1))).