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Chatzipantelidis, Panagiotis

Finite volume methods for elliptic PDE’s: a new approach. (English) Zbl 1041.65087

M2AN, Math. Model. Numer. Anal. 36, No. 2, 307-324 (2002).
A new framework for a finite volume (box scheme) approximation of symmetric second order elliptic problems is proposed and studied. The approximation is viewed as Petrov-Galerkin method where the solution space consistes of continuous piecewise linear functions, while the test space consistes of discontinuous piecewise polynomials. Two choices of test spaces are proposed, one leads to a known method and another produces a new approximation. The most interesting part of the paper is the reduction of the error analysis of the proposed schemes to an analysis of a perturbed standard finite element scheme. This new approach produces optimal error estimates in a discrete \(H^1\)-norm.
Reviewer: Raico R. D. Lazarov (College Station)

Cited in 52 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Keywords:

finite volume methods; error estimates; second order elliptic equation; Petrov-Galerkin method; finite elements
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References:

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