A FINITE ELEMENT METHOD USING SIF FOR CORNER SINGULARITIES WITH AN NEUMANN BOUNDARY CONDITION

다국어 초록 (Multilingual Abstract)

In [8] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary con- dition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which con- verges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

참고문헌 (Reference)

1 김석찬, "Remarks on finite element methods for corner singularities using SIF" 호남수학회 38 (38): 661-674, 2016

2 H. Blum, "On nite element methods for elliptic equations on domains with corners" 28 : 53-63, 1982

3 F. Hecht, "New development in FreeFem++" 20 (20): 251-265, 2012

4 S. C. Brenner, "Multigrid methods for the computation of singular solutions and stress intensity factor I: Corner singularities" 68 (68): 559-583, 1999

5 P. Grisvard, "Elliptic Problems in Nonsmooth Domains" Pitman 1985

6 Z. Cai, "A nite element method using singular functions for the poisson equation: Corner singularities" 39 : 286-299, 2001

7 Z. Cai, "A nite element method using singular func-tions for Poisson equations: Mixed boundary conditions" 195 : 2635-2648, 2006

8 S. Kim, "A nite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor" 71 : 2330-2337, 2016