二维热传导方程的局部间断Ｇａｌｅｒｋｉｎ有限元方法

辽宁石油化工大学学报 ›› 2012, Vol. 32 ›› Issue (2): 88-90.

二维热传导方程的局部间断Ｇａｌｅｒｋｉｎ有限元方法

张荣培^１，王荣荣^２

１．辽宁石油化工大学理学院，辽宁抚顺１１３００１；
２．辽宁石油化工大学职业技术学院，辽宁抚顺１１３００１

收稿日期:2011-04-21 出版日期:2012-06-25 发布日期:2017-07-06
作者简介:张荣培（１９７８－），男，山东新泰市，讲师，在读博士

Local Discontinuous Galerkin Method for the Two-Dimensional Heat Equation

ZHANG Rong-pei¹, WANG Rong-rong² 

1.College of Sciences, Liaonig Shihua University,Fushun Liaoning 113001, P．R．China; 2.School of Vocational Technology, Liaoning Shihua University,Fushun Liaoning 113001, P．R．China

Received:2011-04-21 Published:2012-06-25 Online:2017-07-06

摘要/Abstract

摘要： 讨论了局部间断Ｇａｌｅｒｋｉｎ有限元方法求解二维热传导方程。通过引入辅助变量将含有二阶导数的热传导方程重新写为一阶偏微分方程组，在空间上用间断有限元离散得到一组常微分方程组，在时间上用显式方法离散，最终给出数值算例验证了该方法的收敛精度。

关键词: 　二维热传导方程 , 　局部间断Ｇａｌｅｒｋｉｎ方法 , 　非结构网格

Abstract: The local discontinuous Galerkin method for the two-dimensional equation was introduced. By introducing the auxiliary variable, the second derivative heat conduction equation equations were rewritten into first-order partial differential equations, then the discontinuous Galerkin method was applied to the system. Finally the method yields ordinary differential equations systems. The explicit method was used for the time discretization. The numerical experiments were presented to verify the accuracy of the method. 

Key words: Two-dimensional heat equation , Local discontinuous Galerkin method , Unstructured meshes

张荣培，王荣荣. 二维热传导方程的局部间断Ｇａｌｅｒｋｉｎ有限元方法[J]. 辽宁石油化工大学学报, 2012, 32(2): 88-90.

ZHANG Rong-pei, WANG Rong-rong. Local Discontinuous Galerkin Method for the Two-Dimensional Heat Equation[J]. Journal of Liaoning Petrochemical University, 2012, 32(2): 88-90.