Two simple derivations of universal bounds for the C.B.S. inequality constant

Owe Axelsson; Radim Blaheta

Applications of Mathematics (2004)

  • Volume: 49, Issue: 1, page 57-72
  • ISSN: 0862-7940

Abstract

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Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.

How to cite

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Axelsson, Owe, and Blaheta, Radim. "Two simple derivations of universal bounds for the C.B.S. inequality constant." Applications of Mathematics 49.1 (2004): 57-72. <http://eudml.org/doc/33174>.

@article{Axelsson2004,
abstract = {Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.},
author = {Axelsson, Owe, Blaheta, Radim},
journal = {Applications of Mathematics},
keywords = {finite element method; $h$- and $p$-refinement; strengthened Cauchy-Bunyakowski-Schwarz inequality; finite element method; -refinement; -refinement; strengthened Cauchy-Bunyakowski-Schwarz inequality},
language = {eng},
number = {1},
pages = {57-72},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two simple derivations of universal bounds for the C.B.S. inequality constant},
url = {http://eudml.org/doc/33174},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Axelsson, Owe
AU - Blaheta, Radim
TI - Two simple derivations of universal bounds for the C.B.S. inequality constant
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 1
SP - 57
EP - 72
AB - Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.
LA - eng
KW - finite element method; $h$- and $p$-refinement; strengthened Cauchy-Bunyakowski-Schwarz inequality; finite element method; -refinement; -refinement; strengthened Cauchy-Bunyakowski-Schwarz inequality
UR - http://eudml.org/doc/33174
ER -

References

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