A Finite Volume Element Method for a Non-Linear Elliptic Problem. Chatzipantelidis, P., Ginting, V., & Lazarov, R. Numerical Linear Algebra with Applications, 12(5-6):515-546, 2005. ![A Finite Volume Element Method for a Non-Linear Elliptic Problem [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex 1 download We consider a finite volume discretization of second-order non-linear elliptic boundary value problems on polygonal domains. Using relatively standard assumptions we show the existence of the finite volume solution. Furthermore, for a sufficiently small data the uniqueness of the finite volume solution may also be deduced. We derive error estimates in H1-, L2- and L∈finity-norm for small data and convergence in H1-norm for large data. In addition a Newton's method is analysed for the approximation of the finite volume solution and numerical experiments are presented.
@article {MR2150166,
AUTHOR = {Chatzipantelidis, P. and Ginting, V. and Lazarov, R.},
TITLE = {A {F}inite {V}olume {E}lement {M}ethod for a {N}on-{L}inear {E}lliptic
{P}roblem},
JOURNAL = {Numerical Linear Algebra with Applications},
VOLUME = {12},
YEAR = {2005},
NUMBER = {5-6},
PAGES = {515-546},
ISSN = {1070-5325},
CODEN = {NLAAEM},
MRCLASS = {65N30},
MRNUMBER = {2150166 (2006f:65115)},
MRREVIEWER = {Tom{\'a}{\v{s}} Roub{\'{\i}}{\v{c}}ek},
DOI = {10.1002/nla.439},
URL = {http://dx.doi.org/10.1002/nla.439},
ABSTRACT="
We consider a finite volume discretization of second-order non-linear elliptic boundary value problems on polygonal domains. Using relatively standard assumptions we show the existence of the finite volume solution. Furthermore, for a sufficiently small data the uniqueness of the finite volume solution may also be deduced. We derive error estimates in <i>H</i><sup>1</sup>-, <i>L</i><sub>2</sub>- and <i>L</i><sub>\infinity</sub>-norm for small data and convergence in <i>H</i><sup>1</sup>-norm for large data. In addition a Newton's method is analysed for the approximation of the finite volume solution and numerical experiments are presented.
"
}
Downloads: 1
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