Finite volume methods for elliptic PDE's : a new approach
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 2, p. 307-324

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.

DOI : https://doi.org/10.1051/m2an:2002014
Classification:  65N30,  65N15
Keywords: finite volume methods, error estimates
@article{M2AN_2002__36_2_307_0,
     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},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {2},
     year = {2002},
     pages = {307-324},
     doi = {10.1051/m2an:2002014},
     zbl = {1041.65087},
     language = {en},
     url = {http://www.numdam.org/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, Volume 36 (2002) no. 2, pp. 307-324. doi : 10.1051/m2an:2002014. http://www.numdam.org/item/M2AN_2002__36_2_307_0/

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