The Singularities for Biharmonic Problem with Corner Singularities
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In [8, 9] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomo- geneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].
Abstract
In [8, 9] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomo- geneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].
참고문헌 (11)
- H. Blum, "On finite element methods for elliptic equations on domains with corners", Computing, 28, pp.53~63 (1982)
- H. Blum, "On the Boundary Value Problem of the Biharmonic Oper-ator on Domains with Angular Corners", Math Meth. in the Appl. Sci, 2, pp.556~581 (1980)
- 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.26352648~ (2006)
- Z. Cai, "Error estimate of a finite element method using stress intensity factor", Computers and Mathematics with Applications, 76, pp.2402~2408 (2018)
- P. Grisvard, "Elliptic Problems in Nonsmooth Domains" (1985), Pitman
- 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)
- S. Kim, "Finite element method to control the domain singularities of Poisson equation using the stress intensity factor : mixed boundary condition", Int. J. Numer. Anal. Model, 14(4-5), pp.500~510 (2017)
- S. Kim, "Extraction formulas of stress intensity factors for the biharmonic equations containing crack singularities", Computers and Mathematics with Applications, 80, pp.1142~1163 (2020)
- B. Szabo, "Introduction to Finite Element Analysis; Formulation, Verifica-tion and Validation" (2011), John Wiley