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Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems

Optimal L_∞ Estimates for Galerkin Methods for Nonlinear Singular Two-point Boundary Value Problems
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摘要 In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions. In this paper, we apply the symmetric Galerkin methods to the numerical solutions of a kind of singular linear two-point boundary value problems. We estimate the error in the maximum norm. For the sake of obtaining full superconvergence uniformly at all nodal points, we introduce local mesh refinements. Then we extend these results to a class of nonlinear problems. Finally, we present some numerical results which confirm our theoretical conclusions.
作者 Xu ZHANG Zhong-ci SHI
机构地区 Nanjing University of Aeronautics and Astronautics LSEC
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第3期719-728,共10页 应用数学学报（英文版）
基金 Supported by the Scientific Research Foundation for the Doctor,Nanjing University of Aeronautics and Astronautics(No.1008-907359)
关键词 singular two-point boundary value problems symmetric Galerkin method maximum norm error estimate superconvergence local mesh refinement singular two-point boundary value problems symmetric Galerkin method maximum norm error estimate superconvergence local mesh refinement
分类号 O241.82 [理学—计算数学]
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参考文献8

  • 1Chen, C.M. Superconvergence of Galerkin solutions for singular nonlinear two-point boundary value prob- lems. Math. Numer. Sinica., 7(2): 113-123 (1985) (in Chinese).
  • 2Ciarlet, P.G., Natterer, F., Varga, R.S. Numerical methods of high-order accuracy for singular nonlinear boundary value problems. Numer. Math., 15:87-99 (1970).
  • 3Ciarlet, P.G., Sehultz, M.H., Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math., 9:394-430 (1966/1967).
  • 4Eisenstat, S.G., Sehreiber, R.S., Schultz, M.H. Finite element methods for spherically symmetric elliptic equations. Yale Computer Science Report, 109 (1977).
  • 5Eriksson, K., Nie, Y.Y. Convergence analysis for a nonsymmetric Galerkin method for a class of singular boundary value problems in one space dimension. Math. Comp., 49(179): 167-186 (1987).
  • 6Eriksson, K., Thom6e, V. Galerkin method for singular boundary value problems in one space dimension. Math. Comput., 42:345-367 (1984).
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Acta Mathematicae Applicatae Sinica
2015年 第3期

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