Finite volume methods for elliptic PDE's : a new approach
Chatzipantelidis, Panagiotis
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002), p. 307-324 / Harvested from Numdam
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We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H 1 -norm and L 2 -norm error estimates.

Publié le : 2002-01-01
DOI : https://doi.org/10.1051/m2an:2002014
Classification:  65N30,  65N15 
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     author = {Chatzipantelidis, Panagiotis},
     title = {Finite volume methods for elliptic PDE's : a new approach},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {36},
     year = {2002},
     pages = {307-324},
     doi = {10.1051/m2an:2002014},
     zbl = {1041.65087},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2002__36_2_307_0}
}

Chatzipantelidis, Panagiotis. Finite volume methods for elliptic PDE's : a new approach. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002) pp. 307-324. doi : 10.1051/m2an:2002014. http://gdmltest.u-ga.fr/item/M2AN_2002__36_2_307_0/

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