YAO Fuxia.Error analysis of finite element solution of KdVB equation based on Crank - Nicolson difference method[J].Journal of Yanbian University,2022,(01):19-24.
基于Crank - Nicolson差分法的KdVB方程有限元解的误差分析
- Title:
- Error analysis of finite element solution of KdVB equation based on Crank - Nicolson difference method
- 文章编号:
- 1004-4353(2022)01-0019-06
- 关键词:
- KdVB方程; Crank - Nicolson差分法; 有限元解; 误差分析
- Keywords:
- KdVB equation; Crank - Nicolson difference method; finite element solution; error analysis
- 分类号:
- O241.1
- 文献标志码:
- A
- 摘要:
- 讨论了KdVB方程近似解的误差估计.首先,利用Crank - Nicolson差分法对KdVB方程的时间变量进行离散,由此得到了KdVB方程全离散的H1误差估计.其次,基于特征正交分解(POD)方法得到了KdVB方程的降维模型; 最后,根据Crank - Nicolson差分法对降维模型的时间变量进行离散,由此得到了降维模型的H1误差估计.
- Abstract:
- The error estimation of the approximate solution of the KdVB equation is discussed.Firstly, the time variables of the KdVB equation are discretized by the Crank - Nicolson difference method, and the H1 error estimation of the full discretization of the KdVB equation is obtained.Secondly, the dimensionality reduction model of the KdVB equation is obtained based on the characteristic orthogonal decomposition(POD)method; Finally, the time variables of the reduced dimension model are discretized according to the Crank - Nicolson difference method, and the H1error estimation of the reduced dimension model is obtained.
参考文献/References:
[1] SAKA B, DA D.Quartic B - spline Galerkin approach to the numerical solution of the KdVB equation[J].Applied Mathematics & Computation, 2009,215(2):746 - 758.
[2] JOHNSON R S.A nonlinear equation incorporating damping and dispersion[J].J Fluid Mech, 1970,42:49 - 60.
[3] BONA J L, SCHONBEK M E.Travelling wave solutions to the Korteweg - de Vries - Burgers equation[J].Proceedings of the Royal Society of Edinburgh, 1985,101(3/4):207 - 226.
[4] ZAKI S I. A quintic B - spline finite elements scheme for the KdVB equation[J].Computer Methods in Applied Mechanics & Engineering, 2000,188(1/3):121 - 134.
[5] SAHU B, ROYCHOUDHURY R.Travelling wave solution of Korteweg - de Vries - Burger's equation[J].Czechoslovak Journal of Physics, 2003,53(6):517 - 527.
[6] DEMIRAY H.A travelling wave solution to the KdV - Burgers equation[J].Applied Mathematics and Computation Elsevier, 2004,154:665 - 670.
[7] HELAL M A, MEHANNA M S.A comparison between two different methods for solving KdV - Burgers equation[J].Chaos Solitons & Fractals, 2006,28(2):320 - 326.
[8] 郭瑞,王周峰,王振华.Kdv浅水波方程的Crank - Nicolson差分格式[J].河南科技大学学报(自然科学版),2012,33(2):70 - 74.
[9] 潘悦悦,吴立飞,杨晓忠.Burgers - Fisher方程改进的交替分段Crank - Nicolson并行差分方法[J].高校应用数学学报A辑,2021,36(2):193 - 207.
[10] GRAD H, HU P N.Unified shock profile in a plasma[J].The Physics of Fluids, 1967,10(12):2596 - 2602.
[11] ROSENAU P.A Quasi - Continuous description of a nonlinear transmission line[J].Physica Scripta, 1986,34(6B):827.
[12] KUNISCH K, VOLKWEIN S.Galerkin proper orthogonal decomposition methods for parabolic problems[J].Numerische Mathematik, 2001,90:117 - 148.
[13] 赵锦玮,朴光日.Navier - Stokes系统降维模型中线性反馈控制的分析与逼近[J].延边大学学报(自然科学版),2020,46(4):295 - 301.
备注/Memo
收稿日期: 2021-11-13
作者简介: 姚富霞(1996—),女,硕士研究生,研究方向为数值计算.
文章编号: 1004-4353(2022)01-0019-06