摘要
针对含小参数的奇异摄动微分方程,应用有限元基函数生成有限维子空间处理变分形式,再依据网格参数自动生成分层网格,得到随机剖分数的自适应网格,较之经典网格能更好地捕捉边界层。使用该方法的数值实验非常好地逼近了真解的边界层,得到了不依赖于摄动参数大小,且一致收敛的高精度有限元计算结果。
For a singularly perturbed differential equation with a small parameter,finite dimensional subspace for the variational form is built with finite element basis functions,and the graded mesh is constructed by a mesh generator.Then an adaptive random partitioned mesh is obtained,which is better to resolve the boundary layer than the classic mesh.This strategy performs perfectly to approximate to the boundary layer of the exact solution in the numerical experiment.Highly accurate finite element result is acquired and it is independent to the perturbed parameter and uniformly convergent.
作者
孙美玲
SUN Mei-ling(Department of Public and Basic Courses,Nantong Vocational University,Nantong 226007,China)
出处
《南通职业大学学报》
2018年第4期62-66,共5页
Journal of Nantong Vocational University
基金
国家自然科学基金项目(11301462)
南通职业大学自然科学研究项目(1512105)
关键词
奇异摄动问题
有限元计算
分层网格
自适应
一致收敛
singularly perturbed problem
finite element computation
graded mesh
adaption
uniform convergence
