# Evaluation of the condition number in linear systems arising in finite element approximations

Alexandre Ern; Jean-Luc Guermond

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 1, page 29-48
- ISSN: 0764-583X

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topErn, Alexandre, and Guermond, Jean-Luc. "Evaluation of the condition number in linear systems arising in finite element approximations." ESAIM: Mathematical Modelling and Numerical Analysis 40.1 (2006): 29-48. <http://eudml.org/doc/249710>.

@article{Ern2006,

abstract = {
This paper derives upper and lower bounds for the $\ell^p$-condition
number of the stiffness matrix resulting from the finite element
approximation of a linear, abstract model problem. Sharp estimates in
terms of the meshsize h are obtained. The theoretical results are
applied to finite element approximations of elliptic PDE's in
variational and in mixed form, and to first-order PDE's approximated
using the Galerkin–Least Squares technique or by
means of a non-standard Galerkin technique in
L1(Ω). Numerical simulations are presented to illustrate the
theoretical results.
},

author = {Ern, Alexandre, Guermond, Jean-Luc},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite elements; condition number; partial differential
equations; linear algebra.; finite elements},

language = {eng},

month = {2},

number = {1},

pages = {29-48},

publisher = {EDP Sciences},

title = {Evaluation of the condition number in linear systems arising in finite element approximations},

url = {http://eudml.org/doc/249710},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Ern, Alexandre

AU - Guermond, Jean-Luc

TI - Evaluation of the condition number in linear systems arising in finite element approximations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/2//

PB - EDP Sciences

VL - 40

IS - 1

SP - 29

EP - 48

AB -
This paper derives upper and lower bounds for the $\ell^p$-condition
number of the stiffness matrix resulting from the finite element
approximation of a linear, abstract model problem. Sharp estimates in
terms of the meshsize h are obtained. The theoretical results are
applied to finite element approximations of elliptic PDE's in
variational and in mixed form, and to first-order PDE's approximated
using the Galerkin–Least Squares technique or by
means of a non-standard Galerkin technique in
L1(Ω). Numerical simulations are presented to illustrate the
theoretical results.

LA - eng

KW - Finite elements; condition number; partial differential
equations; linear algebra.; finite elements

UR - http://eudml.org/doc/249710

ER -

## References

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