Finite volume methods for elliptic PDE's : a new approach

Chatzipantelidis, Panagiotis

ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 2, pp. 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.

Classification : 65N30, 65N15
Mots clés : finite volume methods, error estimates

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