Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations

被引：21
|
作者：
Gao, Huadong [1 ,2 ]
Qiu, Weifeng [3 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China
[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 77卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Nonlinear parabolic equations; Finite element method; Discrete Sobolev embedding inequality; Unconditional convergence; Optimal error analysis; REACTION-DIFFUSION EQUATIONS; GALERKIN METHODS; THERMISTOR EQUATIONS; 2-GRID METHOD; POROUS-MEDIA; TRANSPORT; FLOW; APPROXIMATION; FEMS; CONVERGENCE;
D O I：
10.1007/s10915-018-0643-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove a discrete embedding inequality for the Raviart-Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the proved discrete embedding inequality, we provide an optimal error estimate for linearized mixed finite element methods for nonlinear parabolic equations. Several numerical examples are provided to confirm the theoretical analysis.
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页码：1660 / 1678
页数：19
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