Superconvergence of a discontinuous finite element method for a nonlinear ordinary differential equation

被引：3

作者：

Deng, Kang ^{[1
]}

Xiong, Zhiguang ^{[1
]}

机构：

[1] Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 07期

基金：

中国博士后科学基金;

关键词：

Nonlinear ordinary differential equation; Discontinuous finite element with interpolated coefficients; Characteristic points; Superconvergence; INTERPOLATED COEFFICIENTS; HEAT-EQUATION;

D O I：

10.1016/j.amc.2010.09.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, n-degree discontinuous finite element method with interpolated coefficients for an initial value problem of nonlinear ordinary differential equation is introduced and analyzed. By using the finite element projection for an auxiliary linear problem as comparison function, an optimal superconvergence u - U = O(h(n+2)), n >= 2, at (n + 1)-order characteristic points in each element respectively is proved. Finally the theoretic results are tested by a numerical example. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3511 / 3515

页数：5

共 50 条

[41] A new finite element gradient recovery method: Superconvergence property
Zhang, ZM
Naga, A
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 26 (04) : 1192 - 1213
[42] SUPERCONVERGENCE OF DIFFERENTIAL STRUCTURE FOR FINITE ELEMENT METHODS ON PERTURBED SURFACE MESHES
Dong, Guozhi
Guo, Hailong
Guo, Ting
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2024,
[43] Superconvergence analysis of a conservative mixed finite element method for the nonlinear Klein-Gordon-Schrodinger equations
Shi, Dongyang
Zhang, Houchao
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (04) : 2909 - 2934
[44] Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems
Hui Bi
Chengeng Qian
Journal of Inequalities and Applications, 2017
[45] Convergence and superconvergence analysis of finite element methods for the time fractional diffusion equation
Li, Meng
Shi, Dongyang
Pei, Lifang
APPLIED NUMERICAL MATHEMATICS, 2020, 151 : 141 - 160
[46] Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems
Bi, Hui
Qian, Chengeng
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[47] Superconvergence of triangular quadratic finite element with interpolated coefficients for semilinear parabolic equation
Xiong, Zhiguang
Chen, Chuanmiao
APPLIED MATHEMATICS AND COMPUTATION, 2007, 184 (02) : 901 - 907
[48] Superconvergence of a finite element method for the time-fractional diffusion equation with a time-space dependent diffusivity
Na An
Advances in Difference Equations, 2020
[49] W1,∞-seminorm superconvergence of the block finite element method for the five-dimensional Poisson equation
Liu, Jinghong
AIMS MATHEMATICS, 2023, 8 (12): : 31092 - 31103
[50] The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law
Li, Changpin
Wang, Zhen
MATHEMATICS AND COMPUTERS IN SIMULATION, 2020, 169 : 51 - 73

← 1 2 3 4 5 →