- Volume 23 Issue 2
DOI QR Code
ALGORITHMS TO APPLY FINITE ELEMENT DUAL SINGULAR FUNCTION METHOD FOR THE STOKES EQUATIONS INCLUDING CORNER SINGULARITIES
- JANG, DEOK-KYU (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY) ;
- PYO, JAE-HONG (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY)
- Received : 2019.03.18
- Accepted : 2019.06.18
- Published : 2019.06.25
The dual singular function method [DSFM] is a solver for corner sigulaity problem. We already construct DSFM in previous reserch to solve the Stokes equations including one singulairity at each reentrant corner, but we find out a crucial incorrection in the proof of well-posedness and regularity of dual singular function. The goal of this paper is to prove accuracy and well-posdness of DSFM for Stokes equations including two singulairities at each corner. We also introduce new applicable algorithms to slove multi-singulrarity problems in a complicated domain.
Supported by : Kangwon National University
- Z. Cai and S. C. Kim A finite element method using singular functions for the Poisson equations: corner singularities, SIAM J. Numer. Anal., 39 (2001), 286-299. https://doi.org/10.1137/S0036142999355945
- Z. Cai, S. C. Kim and B. C. Shin, Solution methods for the Poisson equation: corner singularities, SIAM J. SCI. COMPut., 23 (2001), 672-682. https://doi.org/10.1137/S1064827500372778
- J.-H. Pyo, A finite element dual singular function method to solve the Stokes equations including corner singularities, International Journal of Numerical Analysis & Modeling, 12 (2015), 516-535.
- S. C. 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 & Mathematics with Applications, 71 (2016), 2330-2337. https://doi.org/10.1016/j.camwa.2015.12.023
- V.A. Kozlov, V.G. Mazya, and J. Rossmann Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations, American Mathematical Society, (2001).
- H.-J. Choi and J.-R. Kweon, The stationary Navier-Stokes system with no-slip boundary condition on polygons: corner singularity and regularity, Commun. Part. Diff. Eq., 38 (2013), 1532-4133.
- S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods Springer-Verlag, (1994).
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, (1991).
- V. Girault and P.A. Raviart, Finite Element Methods for Navier-stokes Equations, Springer-Verlag (1986).
- G. H. Golub and C. F. Van Loan, Matrix computations, Third Edition, Johns Hopkins University Press, (1996).
- E. Kreyszig, Introductory Functional Analysis with Applications, Willy & Sons. Inc, (1978).