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Original Articles

Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

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Pages 161-196 | Published online: 27 Feb 2008

REFERENCES

  • J.H. Bramble and B.E. Hubbard ( 1962 ). On the formulation of finite difference analogies of the Dirichlet problem for Poisson's equation . Numer. Math. 4 : 313 – 327 .
  • C. G. Ciarlet ( 1991 ). Basic error estimates for elliptic problems . in Finite Element Methods (Part I) ( P.G. Ciarlet and J.L. Lions , eds.), North-Holland , Amsterdam .
  • Q. Fang ( 2003 ). Convergence of finite difference methods for convection-diffusion problems with singular solutions . J. Comput. Appl. Math. 152 : 119 – 131 .
  • M. Krizek and P. Neittaanmaki ( 1987 ). On a global-superconvergence of the gradient of linear triangular elements . J. Comput. Appl. Math. 18 : 221 – 233 .
  • Z.C. Li ( 1998 ). Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities . Kluwer Academic Publishers , Dordrecht .
  • Z.C. Li and S. Wang ( 1999 ). The finite volume method and application in combinations . J. Comp. Appl. Math. 106 : 21 – 53 .
  • Z.C. Li , T. Yamamoto , and Q. Fang ( 2003 ). Superconvergence of solution derivatives for the Shortley–Weller difference approximation of Poisson's equation, Part I. Smoothness problems . J. Comp. Appl. Math. 151 : 307 – 333 .
  • Z.C. Li , H.Y. Hu , Q. Fang , and T. Yamamoto ( 2003 ). Superconvergence of solution derivatives for the Shortley–Weller difference approximation of Poisson's equation, Part II. Singularity problems . Numer. Funct. Anal. Optimiz. 24 : 195 – 221 .
  • Z.C. Li , H.Y. Hu , S. Wang , and Q. Fang ( 2008 ). Superconvergence of solution derivatives of the Shortley–Weller difference approximation to Poisson's equation with Singularity problems on polygonal domains . Appl. Numer. Math. ( in press ).
  • G. Strang and G.J. Fix ( 1973 ). An Analysis of the Finite Element Method . Prentice-Hall , Englewood Cliffs , NJ .
  • T. Yamamoto , Q. Fang , and X. Chen (2001). Superconvergence and nonsuperconvergence of the Shortley–Weller approximations for Dirichlet problems. Numer. Funct. Anal. Optimiz. 22:455–470.
  • T. Yamamoto ( 2001 ). Inversion formulas for tridiagonal matrices with applications to boundary value problems . Numer. Funct. Anal. Optimiz. 22 : 357 – 385 .
  • T. Yamamoto ( 2002 ). Convergence of consistant and inconsistent finite difference schemes and an acceleration technique . J. Comp. Appl. Math. 140 : 849 – 866 .
  • K. Yoshida and T. Tsuchiya ( 2001 ). Recovered derivatives for the Shortley–Weller finite difference approximation . Information 4 : 267 – 277 .

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