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A Finite Element Method Using Dual Singular Functions for Elliptic Boundary Value Problems Including Corner Singularities = Corner 특이점을 포함하고 있는 타원형 편미분 방정식 해의 최적 근사를 위한 dual singular function을 이용한 유한요소법

Deok-kyu Jang 2020년

논문상세정보
인용/피인용
' A Finite Element Method Using Dual Singular Functions for Elliptic Boundary Value Problems Including Corner Singularities = Corner 특이점을 포함하고 있는 타원형 편미분 방정식 해의 최적 근사를 위한 dual singular function을 이용한 유한요소법' 의 주제별 논문영향력
논문영향력 선정 방법
논문영향력 요약
주제
  • Corner singularity
  • Dual singular function method
  • Elliptic boundary value problems
  • Singular function
  • Stress intensity factors
  • finiteelementmethods
동일주제 총논문수 논문피인용 총횟수 주제별 논문영향력의 평균
14 0

0.0%

' A Finite Element Method Using Dual Singular Functions for Elliptic Boundary Value Problems Including Corner Singularities = Corner 특이점을 포함하고 있는 타원형 편미분 방정식 해의 최적 근사를 위한 dual singular function을 이용한 유한요소법' 의 참고문헌

  • [9] D. Braess, Finite elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, 2007.
  • [7] H. Blum and M. Dobrowolski, On finite element methods for elliptic equations on domains with corners, Computing 28 (1982), 53?63.
  • [6] K.-J. Bathe, Finite Element Procedures,Cambridge, 2006.
    [2006]
  • [5] I. Babuska and A. Miller, ※ The post-processing approach in the finite element method ? Part 2: the calculation of stress intensity factors, Int. J. Numer. Meth. Eng. 20 (1984), 1111?1129.
  • [53] B. A. Szabo and Z. Yosibash, ▲ Numerical analysis of singularities in two dimensions. Part 2: computation of generalized flux/stress intensity factors, Int. J. Numer. Meth. Eng. 39 (1996), 409?434.
  • [52] B. A. Szabo and Z. Yosibash, ▲ Numerical analysis of singularities in two dimensions. Part 1: computation of the eigenpairs, Int. J. Numer. Meth. Eng. 38 (1995), 2055?2082.
  • [4] I. Babuska and A. Miller, ※ The post-processing approach in the finite element method ? Part 1: calculation of displacements, stresses and other higher derivatives of the displacements, Int. J. Numer. Meth. Eng. 20 (1984), 1085?1109.
  • [49] E. P. Stephan and W. L. Wendland, Anaugmented Galerkin procedure for the boundary integral method applied to mixed boundary value problems, Appl. Numer. Math. 1 (1985), 121?143.
  • [48] E. P. Stephan and W. L. Wendland, Anaugmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems, Appl. Anal. 18 (1984), 183? 220.
  • [45] R. H. Nochetto and J.-H. Pyo, Optimal relaxation parameter for the Uzawa Method, Numer. Math. 98 (2004), 695?702.
  • [43] MATLAB, version 9.6.0 (R2019a Update 4), Natick, Massachusetts: The MathWorks Inc (2019).
  • [42] E. Kreyszig, Introductory Functional Analysis with Applications, Willy & Sons. Inc, (1978).
  • [3] I. Babuska and W. C. Rheinboldt, ※ A-posteriori error estimates for the finite element method, International Journal for Numerical Methods in Engineering 12 (1978), 1597?1615.
  • [39] V. A. Kondratev, ▲ Boundary problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16 (1967), 209?292.
  • [33] B. Guo and I. Babuska, ※ The hp version of the finite element method, Computational Mechanics 1 (1) (1986), 21?41.
  • [32] G. H. Golub and C. F. Van Loan, Matrix computations, Third Edition, Johns Hopkins University Press, (1996).
  • [31] V. Girault and P. A. Raviart, Finite Element Methods for Navier-stokes Equations, SpringerVerlag, 1986.
  • [2] I. Babuska and W. C. Rheinboldt, ※ Error estimates for adaptive finite element computations, SIAM Journal of Numerical Analysis 15 (1978), 736?754.
  • [28] K. O. Friedrichs and H. B. Keller, A finite difference scheme for generalized Neumann problems. In: Numerical solutions of Partial Differential Equations, Proceedings of the Symposium at University of Maryland, May 3?8, 1965, Academic Press, New York (1966), pp. 1?21.
  • [20] P. G. Ciarlet, The Finite Element Method for elliptic problems, North-Holland, Amsterdam.
  • [1] A. K. Aziz, The mathematical foundations of the Finite Element Method with applications to Partial Differential Equations, Proceedings of a Symposium held at the University of Maryland, Baltimore campus, June 26-30, 1972, Academic Press, New York, pp. 3?363.
  • [14] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag (1991).
  • [13] S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Springer, 2002.
  • [10] S. C. Brenner and L.-Y. Sung, Multigrid methods for the computation of singular solutions and stress intensity factors II: Crack singularities BIT Numerical Mathematics 37 (1997), 623? 643.
  • Variational methods for the solution of problems of equilibrium and vibrations
    49 ( 1943 ) , 1 ? 23
  • V. G. Mazya and J. Rossmann , ▲ Elliptic Boundary Value Problems in Domains with Point Singularities
    RI [1997]
  • The stationary Navier-Stokes system with no-slip boundary condition on polygons : corner singularity and regularity ,
    38 ( [2013]
  • The solution of a Laplacian problem over an L-shaped domain with a singular function boundary integral method
    18 ( [2002]
  • The fourier finite element method for the corner singularity expansion of the heat equation13 ? 30
    69 ( [2015]
  • Spectral problems associated with corner singularities of solutions to elliptic equations
    [2001]
  • Solution methods for the Poisson equation withCorner singularities : numerical results
    23 ( 2 ) ( [2001]
  • S. Gulati and G. I. Wakoff , On the use of singular functions with finite element approximations
    13 ( [1973]
  • P-and Hp-Finite Element Methods : Theory and Applications in Solid and Fluid Mechanics
    0.932638889 [1999]
  • Overcoming corner singularities using multigrid methods1883 ? 1892
    35 ( [1998]
  • Numerical Approximation of Elliptic Interface and Corner Problems , Habilitation-schrift , Rheinischen Friedrich-Wilhelms-Universit at
    [1981]
  • New development in FreeFem++ , Journal of numerical mathematics 20 ( 3-4 )251 ? 266
    https : //doc.freefem.org/introduction/index.html # [2012]
  • Multigrid methods for the computation of singular solutions and stress intensity factors I : corner singularities
    68 ( [1999]
  • K. O. Friedrichs , A finite difference scheme for Neumann and Dirichlet problems
    [1962]
  • Finite element dual singular function methods for Helmholtz and heat equations101 ? 113
    22 ( 2 ) ( [2018]
  • Elliptic Problems in Domains with Piecewise Smooth Boundaries ,
    [1994]
  • Comparison of two methods for the computation of singular solutions in elliptic problems ,
    79 ( [1997]
  • Coefficients of the singularities for elliptic boundary value problems on domains with conical points . III : Finite element methods on polygonal domains
    29 ( [1992]
  • Classification of singular solutions for the Poisson problem with various boundary conditions
    31 ( 4 ) ( [2009]
  • An Analysis of the Finite-Element Method
    41 ( 1 ) ( [1974]
  • Algorithms to apply finite element dual singular function method for the Stokes equations including corner singularities ,
    23 ( 2 ) ( [2019]
  • A. Szabo , and I. Babu ska , Finite element analysis
    [1991]
  • A singular function boundary integral method for the Laplace equation ,
    12 ( [1996]
  • A finite element method using singular functions for the Poisson equation : corner singularities ,
    39 ( 1 ) ( [2001]
  • A finite element method using singular functions for the Poisson equation : Mixed boundary condition , Computer Methods in Applied Mechanics and Engineering 1952635 ? 2648
    [2006]
  • A finite element method using singular functions for Helmholtz equations : Part I13 ? 23
    12 ( [2008]
  • A finite element method using singular functions : interface problems Hokkaido Mathematical Journal
    [2007]
  • A finite element dual singular function method to solve the Stokes equations including corner singularities ,
    12 [2015]
  • 196 ? 199
    30 ( 2 ) ( [2004]