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

Mitsuhiro T. Nakao; Nobito Yamamoto; Seiji Kimura

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

Mitsuhiro T. Nakao^*, Nobito Yamamoto, Seiji Kimura

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 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 language	English
Pages (from-to)	491-500
Number of pages	10
Journal	Journal of Approximation Theory
Volume	93
Issue number	3
Publication status	Published - 1998
Externally published	Yes

ASJC Scopus subject areas

Analysis
Numerical Analysis
Mathematics(all)
Applied Mathematics

Cite this

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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.",

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AU - Nakao, Mitsuhiro T.

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AU - Kimura, Seiji

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

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M3 - Article

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SN - 0021-9045

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JO - Journal of Approximation Theory

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IS - 3

ER -

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

Abstract

ASJC Scopus subject areas

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