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

Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)139-157
Number of pages19
JournalNumerische Mathematik
Volume47
Issue number1
DOIs
Publication statusPublished - 1985 Mar
Externally publishedYes

Fingerprint

Galerkin methods
Galerkin Method
Error Estimates
Derivatives
Gauss Points
Derivative
Lp Estimates
Galerkin Finite Element Method
Superconvergence
Nonlinear Evolution Equations
Finite element method
Jacobi
Knot
Rate of Convergence
Approximate Solution
Exact Solution
Approximation

Keywords

  • Subject Classifications: AMS(MOS): 65N30, CR: G1.8

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Mathematics(all)

Cite this

Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension. / Nakao, Mitsuhiro T.

In: Numerische Mathematik, Vol. 47, No. 1, 03.1985, p. 139-157.

Research output: Contribution to journalArticle

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