Superconvergence analysis of the mixed finite element method for the Rosenau equation

被引：12
|
作者：
Shi, Dongyang [1 ]
Jia, Xu [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 481卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Implicit CN scheme; Mixed FEM; Existence and uniqueness; Stability; Supercloseness and superconvergence; Combination technique; DIFFERENCE SCHEME;
D O I：
10.1016/j.jmaa.2019.123485
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an implicit Crank-Nicolson (CN) formula of the mixed finite element method (FEM) is developed with the bilinear finite element for nonlinear fourth-order Rosenau equation. The stability, existence and uniqueness of the approximate solution of this scheme are proved. Then, unconditional superclose and superconvergence estimates of order O(h(2) + tau(2)) in H-1-norm are derived by the combination technique of interpolation and projection. Finally, some numerical results confirm our theoretical analysis. Here and later h and tau denote the mesh size and the time step, respectively. (C) 2019 Elsevier Inc. All rights reserved.
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页数：19
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