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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then 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 they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.
목차
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참고문헌 (9)
참고문헌 신청
I. Babuska / 1979 / Direct and inverse error estimates for nite elements with mesh re nements / Numer. Math 33:447~471
H. Blum / 1982 / On nite element methods for elliptic equations on domains with corners / Computing 28:53~63
Z. Cai / 2001 / A nite element method using singular functions for the poisson equation: Corner singularities / SIAM J. Numer. Anal 39:286~299
Z. Cai / 2006 / A nite element method using singular functions for Poisson equations: Mixed boundary conditions / Comput. Methods Appl. Mech. Engrg 195:2635~2648
G. J. Fix / 1973 / On the use of singular functions with nite elements approximations / J. Comput. Phy 13:209~228
H. Blum / 1982 / On nite element methods for elliptic equations on domains with corners / Computing 28:53~63
Z. Cai / 2001 / A nite element method using singular functions for the poisson equation: Corner singularities / SIAM J. Numer. Anal 39:286~299
Z. Cai / 2006 / A nite element method using singular functions for Poisson equations: Mixed boundary conditions / Comput. Methods Appl. Mech. Engrg 195:2635~2648
G. J. Fix / 1973 / On the use of singular functions with nite elements approximations / J. Comput. Phy 13:209~228
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