Some Remarks on Convergence of Two-Grid Method under Grid Adaption

• Main Authors: Gin-Tzong Shy, 施金宗
• Other Authors: Chen-Yao Lai
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/45828250809163992507

碩士 === 國立中正大學 === 應用數學研究所 === 87 === In the thesis, first of all, we apply optimal mesh redistribution algorithm for the Galerkin's finite element method and the least squares finite element method to find the asymptotic optimal mesh. After then, we add a point to the midpoint of every subinterval, and perform two-grid method on this new mesh. We shall investigate some convergence properties of two-grid method on this optimal mesh, and compare the convergence property of two-grid method between uniform and optimal mesh. Our numerical results shows that the convergence rate of two-grid method on optimal mesh is better than that on uniform mesh. We also study the smoothing and approximation properties via some numerical experiment.