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On the finite volume element method. (English) Zbl 0731.65093
The author considers the problem -·(Au)=f on a polygonal domain Ω 2 with u=0 on Γ 0 , Au·n=g on Γ 1 , Γ 0 Γ 1 =Ω, A uniformly elliptic. The author considers piecewise linear functions v on a regular triangularization of Ω, b ij (v)=- γ ij (Av)·n ij ds for γ ij an edge connecting triangle interior points (consistently taken as either circumcenters, orthocenters, incenters, or centroids), and the linear operator B defined by (Bv) i = j b ij (v)· He gives conditions under which B will be uniformly elliptic, and under those conditions derives estimates on the discretization error.

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
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