弹性动力学问题的混合间断时空有限元法

数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1179-1190.

弹性动力学问题的混合间断时空有限元法

何斯日古楞|李宏

内蒙古大学数学科学学院 |呼和浩特 |010021

收稿日期:2011-07-18 修回日期:2012-05-18 出版日期:2012-12-25 发布日期:2012-12-25
基金资助:
国家自然科学基金(11061021)、内蒙古自治区高等学校科学研究项目(NJ10006)、内蒙古大学研究生培养基金和内蒙古自然科学基金(2012MS0106)资助

Mixed Space--time Discontinuous Galerkin Method for Elastodynamics

HE Siriguleng, LI Hong

School of Mathematical Science, Inner Mongolia University, Hohhot 010021

Received:2011-07-18 Revised:2012-05-18 Online:2012-12-25 Published:2012-12-25
Supported by:
国家自然科学基金(11061021)、内蒙古自治区高等学校科学研究项目(NJ10006)、内蒙古大学研究生培养基金和内蒙古自然科学基金(2012MS0106)资助

摘要/Abstract

摘要：

针对弹性动力学问题从更自然的二阶双曲型方程出发, 构造了同时求解位移和速度的一种时间间断、空间连续的混合间断时空有限元格式. 其次, 利用有限差分和有限元方法相结合的技巧分析了格式的稳定性及收敛性, 并得到了时间最大模、空间应变能量、动能以及总机械能模最优误差估计.

关键词: 弹性动力学问题, 间断时空有限元法, 稳定性, 最优误差估计

Abstract:

Mixed space--time discontinuous Galerkin method, discontinuous in time and continuous in space, for elastodynamics is developed based on the more natural framework of second order hyperbolic equations. The displacement and velocity are solved simultaneously by the method. Then, the stability and convergence of the scheme are analyzed by using the technique of combination of finite difference and finite element methods. The optimal error estimates in time maximum norm and space strain energy, kinetic energy and total mechanical energy norms are obtained.

Key words: Space--time discontinuous Galerkin method, Stability, Optimal error estimate

中图分类号:

65M05

何斯日古楞, 李宏. 弹性动力学问题的混合间断时空有限元法[J]. 数学物理学报, 2012, 32(6): 1179-1190.

HE Siriguleng, LI Hong. Mixed Space--time Discontinuous Galerkin Method for Elastodynamics[J]. Acta mathematica scientia,Series A, 2012, 32(6): 1179-1190.

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