Sif and Finite Element Solutions for Corner Singularities
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In [7, 8] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary condi- tions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accu- rate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.
Abstract
In [7, 8] they introduced a new finite element method for ac- curate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary condi- tions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accu- rate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.
참고문헌 (8)
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- Z. CAI AND S.C. KIM, "A finite element method using singular functions for the poisson equation: Corner singularities", SIAM J. Numer. Anal., 39, pp.286~299 (2001)[DOI]
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- 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 AND H.C. LEE, "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)[DOI]
- S. KIM AND H.-C. LEE, "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)