Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension

Mitsuhiro T. Nakao*

*この研究の対応する著者

研究成果: Article査読

23 被引用数 (Scopus)

抄録

A semidiscrete Galerkin finite element method is defined and analyzed for nonlinear evolution equations of Sobolev type in a single space variable. Optimal order Lp error estimates are derived for 2≦p≦∞. And it is shown that the rates of convergence of the approximate solution and its derivative are one order better than the optimal order at certain spatial Jacobi and Gauss points, respectively. Also the standard nodal superconvergence results are established. Futher, it is considered that an a posteriori procedure provides superconvergent approximations at the knots for the spatial derivatives of the exact solution.

本文言語English
ページ(範囲)139-157
ページ数19
ジャーナルNumerische Mathematik
47
1
DOI
出版ステータスPublished - 1985 3月
外部発表はい

ASJC Scopus subject areas

  • 計算数学
  • 応用数学
  • 数学 (全般)

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