Multigrid and Adaptive Methods for Computing Singular Solutions of Laplace Equation on Corner Domains

• Main Authors: Lee, Wei-Jen, 李偉任
• Other Authors: Wu, Chin-Tien
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/77603040683327370289

碩士 === 國立交通大學 === 應用數學系數學建模與科學計算碩士班 === 98 === Elliptic boundary value problems on domain with corners have singular behavior near the corners. Such singular behavior affect the accuracy of the finite element method throughout the whole domain. For the Poisson equation with homogeneous Dirichlet boundary conditions defined on a polygonal domain with re-entrant corners, it is well known that the solution has the singular function u=w+ks representation ,where w is the regular part of the solution and s are known as singular functions that depend only on the corresponding re-entrant angles. Coefficients k known as the stress intensity factors in the context of mechanics can be expressed in terms of u by extraction formula, where s- are known as dual singular funciton. Accurate calculation of these quantities is of great importance in many practical engineering problems. Similar singular function representations hold for the solutions of interface,biharmonic,elasticity, and evolution problems in [1, 2].