摘要
自适应网格对很多问题的数值方法在存储空间、计算量和精度方面影响很大.以一维和二维Allen-Cahn方程为例,基于移动网格法,建立了线性有限元数值模型.数值结果表明在移动网格下的数值解能够很好地保持原方程固有的能量稳定性质,高分辨率地捕捉变化特征,提高计算效率,验证了该方法的有效性和可行性.移动网格法也可用于数值积分、常微分方程数值解等问题.
Adaptive meshes have great influence on the storage space,computation amount and accuracy of numerical methods for many problems.Based on the moving mesh method,the linear finite element numerical models of one-and two-dimensional Allen-Cahn equations are established.The numerical results show that the numerical solution under the moving grid can keep the inherent energy stability of the original equation well,capture the variation characteristics with high resolution,and improve the computational efficiency,which verifies the effectiveness and feasibility of the proposed method.The moving mesh method can also be used for numerical integration and ordinary differential numerical solutions.
作者
卢长娜
钱存鑫
常胜祥
LU Chang-na;QIAN Cun-xin;CHANG Sheng-xiang(College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)
出处
《数学的实践与认识》
2022年第12期230-236,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(11801280)
江苏省自然科学基金(BK20180780)
2021年江苏省第一批一流课程(苏教高函[2021]9号)。
