Energy-stable finite element method for a class of nonlinear fourth-order parabolic equations

被引：1

作者：

Tian, Jia ^{[1
]}

He, Mingyan ^{[1
]}

Sun, Pengtao ^{[2
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

[2] Univ Nevada Las Vegas, Dept Math Sci, Las Vegas, NV 89154 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 438卷

关键词：

Nonlinear fourth-order parabolic equations; Energy stability; Finite element method; Crank-Nicolson scheme; Semi-discrete; Optimal convergence; DIFFERENCE SCHEME; ADDITIVE NOISE; NEURAL FIELDS; DIFFUSION; DYNAMICS; SYSTEMS; ONSET;

D O I：

10.1016/j.cam.2023.115576

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an energy-stable finite element method with the Crank-Nicolson type of temporal discretization scheme is developed and analyzed for a class of nonlinear fourth-order parabolic equations (including the Swift-Hohenberg (SH) equation and the extended Fisher-Kolmogorov (EFK) equation). In addition to the energy stability properties, the optimal spatial convergence properties in both L infinity(L2)-and L infinity(H1)-norm and the second-order temporal approximation rate are also obtained for numerical solutions approximating to the real solution and its Laplacian for the developed energy-stable finite element method in both semi-and fully discrete schemes. Numerical experiments are carried out to validate all attained theoretical results.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：23

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