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In [15] they introduced a new finite element method for accurate 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 condition, 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 converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.
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참고문헌 (23)
참고문헌 신청
I. Babuska / 1979 / Direct and inverse error estimates for finite elements with mesh refinements / Numer. Math. 33:447~471
H. Blum / 1982 / On finite element methods for elliptic equations on domains with corners / Computing 28:53~63
M. Bourlard / 1992 / Coeffcients of the singularities for elliptic boundary value problems on domains with conical points III. Finite element methods on polygonal domains / SIAM Numer. Anal. 29:136~155
S. C. Brenner / 1999 / Multigrid methods for the computation of singular solutions and stress intensity factor I: Corner singularities / Math. Comp. 68(226):559~583
S. C. Brenner / 2003 / Multigrid methods for the computation of sin-gular solutions and stress intensity factors III: Interface singularities / Comput. Methods Appl. Mech. Engrg 192:4687~4702
H. Blum / 1982 / On finite element methods for elliptic equations on domains with corners / Computing 28:53~63
M. Bourlard / 1992 / Coeffcients of the singularities for elliptic boundary value problems on domains with conical points III. Finite element methods on polygonal domains / SIAM Numer. Anal. 29:136~155
S. C. Brenner / 1999 / Multigrid methods for the computation of singular solutions and stress intensity factor I: Corner singularities / Math. Comp. 68(226):559~583
S. C. Brenner / 2003 / Multigrid methods for the computation of sin-gular solutions and stress intensity factors III: Interface singularities / Comput. Methods Appl. Mech. Engrg 192:4687~4702
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