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Zbl 0729.65086
Cai, Zhiqiang; Mandel, Jan; McCormick, Steve
The finite volume element method for diffusion equations on general triangulations. (English)
[J] SIAM J. Numer. Anal. 28, No.2, 392-402 (1991). ISSN 0036-1429; ISSN 1095-7170/e

The authors prove the convergence and get a priori error estimates for the approximation of diffusion equations of the form $-\nabla (A\nabla u)=f$ in $\Omega$, $u=0$ on $\partial \Omega$ by the finite volume element method. The two dimensional domain $\Omega$ is assumed to be polygonal and exactly covered by a general Delaunay-Voronoi triangulation with no interior angle larger than 90$\circ$. Thus they prove O(h) estimates of the error in a discrete $H\sp 1$-seminorm and a $O(h\sp 2)$ estimate under an additional assumption concerning local uniformity of the triangulation.
[M.Bernadou (Le Chesnay)]

MSC 2000:: *65N35 Collocation methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
65N50 Mesh generation and refinement (BVP of PDE)
76R50 Diffusion
35J25 Second order elliptic equations, boundary value problems

Keywords: convergence; error estimates; diffusion equations; finite volume element method; Delaunay-Voronoi triangulation

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