A FINITE ELEMENT METHOD USING SIF FOR CORNER SINGULARITIES WITH AN NEUMANN BOUNDARY CONDITION
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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 (8)
- H. Blum, "On finite element methods for elliptic equations on domains with corners", Computing, 28, pp.53~63 (1982)
- S. C. Brenner, "Multigrid methods for the computation of singular solutions and stress intensity factor I: Corner singularities", Math. Comp, 68(226), pp.559~583 (1999)
- Z. Cai, "A finite element method using singular functions for the poisson equation: Corner singularities", SIAM J. Numer. Anal, 39, pp.286~299 (2001)
- Z. Cai, "A finite element method using singular func-tions for Poisson equations: Mixed boundary conditions", Comput. Methods Appl. Mech. Engrg, 195, pp.2635~2648 (2006)
- P. Grisvard, "Elliptic Problems in Nonsmooth Domains" (1985), Pitman
- F. Hecht, "New development in FreeFem++", J. Numer. Math, 20(3-4), pp.251~265 (2012)
- 김석찬, "Remarks on finite element methods for corner singularities using SIF", 호남수학학술지, 38(3), pp.661~674 (2016), 호남수학회
- S. Kim, "A finite element method for computing accurate solutions for Poisson equations with corner singularities using the stress intensity factor", Computers and Mathematics with Applications, 71, pp.2330~2337 (2016)