On the Best Constant in the Error Bound for the H1 0-Projection into Piecewise Polynomial Spaces

Mitsuhiro T. Nakao, Nobito Yamamoto, Seiji Kimura

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

Explicit a priori error bounds for the approximation by the H1 0-projection into piecewise polynomial spaces are given. In particular, for the quadratic approximation, the optimal constant is derived, and a nearly optimal value for the cubic is obtained. These constants play an important role in the numerical verification method of finite element solutions for nonlinear elliptic equations.

Original languageEnglish
Pages (from-to)491-500
Number of pages10
JournalJournal of Approximation Theory
Volume93
Issue number3
Publication statusPublished - 1998
Externally publishedYes

Fingerprint

A Priori Error Bounds
Optimal Constants
Numerical Verification
Quadratic Approximation
Best Constants
Nonlinear Elliptic Equations
Piecewise Polynomials
Finite Element Solution
Error Bounds
Polynomials
Projection
Approximation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

On the Best Constant in the Error Bound for the H1 0-Projection into Piecewise Polynomial Spaces. / Nakao, Mitsuhiro T.; Yamamoto, Nobito; Kimura, Seiji.

In: Journal of Approximation Theory, Vol. 93, No. 3, 1998, p. 491-500.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Yamamoto, Nobito ; Kimura, Seiji. / On the Best Constant in the Error Bound for the H1 0-Projection into Piecewise Polynomial Spaces. In: Journal of Approximation Theory. 1998 ; Vol. 93, No. 3. pp. 491-500.
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