Mesh Redistribution in the Finite Element Methods for One-dimensional Hyperbolic Equations

• Main Authors: Ming-Yu Cheng, 鄭明佑
• Other Authors: Tsu-Fen Chen
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/39235989753030012573

碩士 === 國立中正大學 === 應用數學研究所 === 97 === This work concerns the solutions of one-dimensional time dependent linear hyperbolic equations and Burgers'' equations based on the the finite element approximations. We also consider the redistribution approach to generate the optimal grids. The idea is to adjust the position of the grid points and produce a mesh with the same number of unknows, but more appropriately graded for the given problem. In this study, time varying optimal grids based on mesh redistribution will be considered. Numerical results of the finite element methods with upwinding and optimal graded mesh will be provided. Discussions and improvements of the algorithms will also be presented.