一类热传导自由边界问题的多尺度有限元法求解  

Multiscale finite element computation for a type of free boundary problem in heat conduction

作　　者：江山[1] 于陆洋 孙美玲[3] JIANG Shan;YU Luyang;SUN Meiling(School of Science Nantong University,Nantong 226019 China;School of Mathematics Science,Uangzhou University,Yangzhou 225002China;Department of Public Education,Nantong Vocational University,Nantong 226007,China)

机构地区：[1]南通大学理学院,江苏南通226019 [2]扬州大学数学科学学院,江苏扬州225002 [3]南通职业大学公共教学部,江苏南通226007

出　　处：《扬州大学学报（自然科学版）》2018年第1期11-14,25,共5页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金面上资助项目(11771224);江苏省高校青蓝工程优秀青年骨干教师资助项目;江苏省高校优秀中青年教师公派赴境外研修资助项目

摘　　要：针对一类热传导的自由边界问题,首先利用变量变换规范求解区域,然后采用多尺度有限元法结合Shishkin网格离散化模型,并通过龙格-库塔法模拟非线性边界.两种方案交替迭代,以处理非驻定热传导自由边界问题.数值算例结果表明,该算法既可保证高阶精度,又可节约计算资源,能有效改进原模型的应用模拟.For a type of free boundary problem in the heat conduction,first a variable transformation is used to normalize the irregular domain.Then the multiscale finite element method on Shishkin grid is applied to solve it.For the nonlinear free boundary,the Runge-Kutta method is provided.As a consequence,these two alternative iterations are proposed for the time-dependent heat model.The results of numerical experiments show the accuracy and efficiency of the algorithm.It presents an effective improvement for the model application.

关 键 词：多尺度有限元法 热传导自由边界问题 SHISHKIN网格 龙格-库塔法 

分 类 号：O241.82[理学—计算数学]