A SECOND-ORDER STABILIZATION METHOD FOR LINEARIZING AND DECOUPLING NONLINEAR PARABOLIC SYSTEMS

被引：5

作者：

Li, Buyang ^{[1
]}

Ueda, Yuki ^{[1
,2
]}

Zhou, Guanyu ^{[3
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Hong Kong, Peoples R China

[2] Waseda Univ, Waseda Res Inst Sci & Engn, Fac Sci & Engn, Tokyo, Japan

[3] Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, 4,Sect 2,North Jianshe Rd, Chengdu, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2020年 / 58卷 / 05期

关键词：

nonlinear parabolic system; stabilization; linearization; decoupling; convergence; FINITE-ELEMENT APPROXIMATION; ERROR ANALYSIS; GRADIENT FLOW; EQUATIONS; CONVERGENCE; EVOLUTION;

D O I：

10.1137/19M1296136

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new time discretization method for strongly nonlinear parabolic systems is constructed by combining the fully explicit two-step backward difference formula and a second-order stabilization of wave type. The proposed method linearizes and decouples a nonlinear parabolic system at every time level, with second-order consistency error. The convergence of the proposed method is proved by combining energy estimates for evolution equations of parabolic and wave types with the generating function technique that is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.

引用

页码：2736 / 2763

页数：28

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