High order spline finite element method for the fourth-order parabolic equations

被引：2
作者：
Du, Shaohong [1 ]
Cheng, Yongping [1 ]
Li, Mingjun [1 ]
机构：
[1] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2023年 / 184卷
关键词：
Fourth-order parabolic equation; High-order spline element method; L-2 and H-2 error estimates; Stability condition; GALERKIN METHODS; APPROXIMATIONS;
D O I：
10.1016/j.apnum.2022.11.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we concern with the development of error estimates for high-order spline finite element approximation to a class of fourth-order parabolic equations. The L-2 estimates for semi-discrete scheme are derived by constructing two auxiliary problems (one is a steady-state problem, the other is similar to the primal problem) and by using the structure of solutions of the second-order ordinary differential equation and the similarity theory of matrices, and are optimal in terms of the regularity of the exact solution. The H-2 energy estimates for spline-element central difference approximation are established under a condition of stability (for explicit scheme), and are optimal for space variable in H-2-norm and for time variable in H-1,H-infinity- norm. Numerical examples are presented to validate the theory. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
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收藏
页码：496 / 511
页数：16
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