摘要
研究含极小摄动参数的一维对流扩散方程,应用多尺度有限元的高效计算格式求其数值解.构造的多尺度基函数能细致模拟边界层,迭代的自适应优化网格能精确逼近过渡点,通过Matlab模块化编程,从而在宏观尺度节省计算消耗,得到了范数度量下的一致收敛精确化模拟.
For a one-dimensional convection-diffusion equation with an extremely small perturbed parameter,a multiscale finite element scheme is proposed for its efficient numerical solution.The multiscale basis functions are able to simulate the boundary layers subtly,the adaptively optimal meshes are trend to approximate the transient location precisely,and we apply Matlab programing.As a result,computational costs are saved on the macroscopic scales and the uniformly convergent accuracy is realized for testing norms.
作者
孙美玲
王晓莹
江山
SUN Meiling;WANG Xiaoying;JIANG Shan(Department of Mathematics,Nantong Vocational University,Nantong 226007,China;School of Science,Nantong University,Nantong 226019,China)
出处
《湘潭大学学报（自然科学版）》
CAS
2022年第2期63-71,共9页
Journal of Xiangtan University(Natural Science Edition)
基金
国家自然科学基金面上项目(11771224)
南通市基础科学研究指令性项目(JC2021123)
南通职业大学高等教育教改研究课题(2019-YB-02)。
关键词
奇异摄动边界层
优化网格
多尺度有限元法
一致收敛
singular perturbation boundary layers
optimal meshes
multiscale finite element method
uniform convergence
