# A comparison of some efficient numerical methods for a nonlinear elliptic problem

Open Mathematics (2012)

- Volume: 10, Issue: 1, page 217-230
- ISSN: 2391-5455

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topBalázs Kovács. "A comparison of some efficient numerical methods for a nonlinear elliptic problem." Open Mathematics 10.1 (2012): 217-230. <http://eudml.org/doc/269774>.

@article{BalázsKovács2012,

abstract = {The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them and analyzed their behavior, efficiency and mesh independence. We also compare the theoretical results to the numerical ones, and finally we propose some improvements which we also investigate.},

author = {Balázs Kovács},

journal = {Open Mathematics},

keywords = {Radiative cooling problem; Iterative methods; Stepwise variable preconditioning; Numerical experiments; radiative cooling problem; iterative methods; stepwise variable preconditioning; numerical experiments; nonlinear elliptic problem; gradient method; Newton method; quasi-Newton method},

language = {eng},

number = {1},

pages = {217-230},

title = {A comparison of some efficient numerical methods for a nonlinear elliptic problem},

url = {http://eudml.org/doc/269774},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Balázs Kovács

TI - A comparison of some efficient numerical methods for a nonlinear elliptic problem

JO - Open Mathematics

PY - 2012

VL - 10

IS - 1

SP - 217

EP - 230

AB - The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them and analyzed their behavior, efficiency and mesh independence. We also compare the theoretical results to the numerical ones, and finally we propose some improvements which we also investigate.

LA - eng

KW - Radiative cooling problem; Iterative methods; Stepwise variable preconditioning; Numerical experiments; radiative cooling problem; iterative methods; stepwise variable preconditioning; numerical experiments; nonlinear elliptic problem; gradient method; Newton method; quasi-Newton method

UR - http://eudml.org/doc/269774

ER -

## References

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