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The finite volume element method for diffusion equations on general triangulations. (English) Zbl 0729.65086
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.

65N35Spectral, collocation and related methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N50Mesh generation and refinement (BVP of PDE)
76R50Diffusion (fluid mechanics)
35J25Second order elliptic equations, boundary value problems
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