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波动问题的非标准有限元

Nonstandard finite elements for wave problems
课程网址: http://videolectures.net/8ecm2021_perugia_finite_elements/  
主讲教师: Ilaria Perugia
开课单位: 维也纳大学
开课时间: 2021-07-06
课程语种: 英语
中文简介:
有限元是一种强大、灵活和稳健的方法,用于偏微分方程解的数值逼近。在他们的标准版本中,它们是基于感兴趣领域分区上的分段多项式函数。连续性要求可能由精确解的规律性决定。通过打破这些限制,已经开发出专门针对手头问题的新方法,以便更好地再现精确解的物理性质,增强稳定性,并提高精度和计算成本。基于时空范式的波传播问题的非标准有限元近似将是本次演讲的重点。
课程简介: Finite elements are a powerful, flexible, and robust class of methods for the numerical approximation of solutions to partial differential equations. In their standard version, they are based on piecewise polynomial functions on a partition of the domain of interest. Continuity requirements are possibly dictated by the regularity of the exact solutions. By breaking these constraints, new methods that are specifically tailored to the problem at hand have been developed in order to better reproduce physical properties of the exact solutions, to enhance stability, and to improve accuracy vs. computational cost. Nonstandard finite element approximations of wave propagation problems based on the space-time paradigm will be the focus of this talk.
关 键 词: 有限元; 偏微分方程; 连续性要求
课程来源: 视频讲座网
数据采集: 2021-11-22:nkq
最后编审: 2021-11-22:nkq
阅读次数: 33