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

Panagiotis Chatzipantelidis — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

Finite Volume Methods for Elliptic PDE's: A New Approach

Panagiotis Chatzipantelidis — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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 norm and norm error estimates.

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